%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG116+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n017.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 18:29:29 EDT 2022 % Result : Theorem 51.19s 51.39s % Output : Proof 51.50s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.12 % Problem : ALG116+1 : TPTP v8.1.0. Released v2.7.0. % 0.03/0.12 % Command : run_zenon %s %d % 0.12/0.33 % Computer : n017.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 600 % 0.12/0.33 % DateTime : Wed Jun 8 06:37:18 EDT 2022 % 0.12/0.33 % CPUTime : % 51.19/51.39 (* PROOF-FOUND *) % 51.19/51.39 % SZS status Theorem % 51.19/51.39 (* BEGIN-PROOF *) % 51.19/51.39 % SZS output start Proof % 51.19/51.39 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))))))))))))))))))))))))))). % 51.19/51.39 Proof. % 51.19/51.39 assert (zenon_L1_ : (~((h4 (e10)) = (e20))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H12 zenon_H13 zenon_H14. % 51.19/51.39 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (e10)) = (e20))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H12. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H13. % 51.19/51.39 cut (((op2 (e23) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 51.19/51.39 cut (((h4 (e10)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H16. apply refl_equal. % 51.19/51.39 apply zenon_H15. apply sym_equal. exact zenon_H14. % 51.19/51.39 (* end of lemma zenon_L1_ *) % 51.19/51.39 assert (zenon_L2_ : (~((e13) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H17. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L2_ *) % 51.19/51.39 assert (zenon_L3_ : (~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H18 zenon_H19. % 51.19/51.39 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H1a. apply sym_equal. exact zenon_H19. % 51.19/51.39 (* end of lemma zenon_L3_ *) % 51.19/51.39 assert (zenon_L4_ : (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e10) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H1b zenon_H1c zenon_H1d zenon_H19. % 51.19/51.39 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e10) (e11)) = (op1 (e13) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H1b. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H1c. % 51.19/51.39 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 51.19/51.39 cut (((e10) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 51.19/51.39 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e10) = (op1 (e10) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H1e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H1f. % 51.19/51.39 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 51.19/51.39 cut (((op1 (e10) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H21 zenon_H1d). % 51.19/51.39 apply zenon_H20. apply refl_equal. % 51.19/51.39 apply zenon_H20. apply refl_equal. % 51.19/51.39 apply (zenon_L3_); trivial. % 51.19/51.39 (* end of lemma zenon_L4_ *) % 51.19/51.39 assert (zenon_L5_ : ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H22 zenon_H23 zenon_H24. % 51.19/51.39 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 51.19/51.39 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((op1 (e10) (e10)) = (op1 (e10) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H24. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H25. % 51.19/51.39 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 51.19/51.39 cut (((op1 (e10) (e12)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e10) (e12)) = (e10)) = ((op1 (e10) (e12)) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H27. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H22. % 51.19/51.39 cut (((e10) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 51.19/51.39 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H26. apply refl_equal. % 51.19/51.39 apply zenon_H28. apply sym_equal. exact zenon_H23. % 51.19/51.39 apply zenon_H26. apply refl_equal. % 51.19/51.39 apply zenon_H26. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L5_ *) % 51.19/51.39 assert (zenon_L6_ : (~((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H29 zenon_H1c. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((op1 (e13) (op1 (e13) (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H2a. apply sym_equal. exact zenon_H1c. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L6_ *) % 51.19/51.39 assert (zenon_L7_ : (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e10) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H2b zenon_H2c zenon_H2d zenon_H1c. % 51.19/51.39 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e10) (e10)) = (op1 (e10) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H2b. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2c. % 51.19/51.39 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 51.19/51.39 cut (((e12) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((e12) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H2e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2f. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H31 zenon_H2d). % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply (zenon_L6_); trivial. % 51.19/51.39 (* end of lemma zenon_L7_ *) % 51.19/51.39 assert (zenon_L8_ : (~((e10) = (e10))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H32. % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L8_ *) % 51.19/51.39 assert (zenon_L9_ : ((op1 (e11) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e12)) -> (~((e10) = (e12))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H33 zenon_H34 zenon_H35. % 51.19/51.39 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.19/51.39 cut (((e12) = (e12)) = ((e10) = (e12))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H35. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H36. % 51.19/51.39 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.39 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e11) (e10)) = (e10)) = ((e12) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H38. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H33. % 51.19/51.39 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.39 cut (((op1 (e11) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H39 zenon_H34). % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L9_ *) % 51.19/51.39 assert (zenon_L10_ : (~((e11) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H3a. % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L10_ *) % 51.19/51.39 assert (zenon_L11_ : ((op1 (e10) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e13)) -> (~((e11) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H3b zenon_H3c zenon_H3d. % 51.19/51.39 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.39 cut (((e13) = (e13)) = ((e11) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H3d. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3e. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e10) (e10)) = (e11)) = ((e13) = (e11))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H3f. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3b. % 51.19/51.39 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H40 zenon_H3c). % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L11_ *) % 51.19/51.39 assert (zenon_L12_ : ((op1 (e11) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e10) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H33 zenon_H41 zenon_H42. % 51.19/51.39 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.39 cut (((e13) = (e13)) = ((e10) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H42. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3e. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e11) (e10)) = (e10)) = ((e13) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H43. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H33. % 51.19/51.39 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.39 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H44 zenon_H41). % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L12_ *) % 51.19/51.39 assert (zenon_L13_ : (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H45 zenon_H46 zenon_H47. % 51.19/51.39 cut (((op1 (e10) (e11)) = (e13)) = ((op1 (e10) (e11)) = (op1 (e11) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H45. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H46. % 51.19/51.39 cut (((e13) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 51.19/51.39 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H20. apply refl_equal. % 51.19/51.39 apply zenon_H48. apply sym_equal. exact zenon_H47. % 51.19/51.39 (* end of lemma zenon_L13_ *) % 51.19/51.39 assert (zenon_L14_ : (~((e12) = (e12))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H37. % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L14_ *) % 51.19/51.39 assert (zenon_L15_ : ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e13)) = (e13)) -> (~((e12) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H49 zenon_H4a zenon_H4b. % 51.19/51.39 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.39 cut (((e13) = (e13)) = ((e12) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H4b. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3e. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e10) (e13)) = (e12)) = ((e13) = (e12))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H4c. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H49. % 51.19/51.39 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.39 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H4d zenon_H4a). % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L15_ *) % 51.19/51.39 assert (zenon_L16_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e12))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H4e zenon_H49 zenon_H35. % 51.19/51.39 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.19/51.39 cut (((e12) = (e12)) = ((e10) = (e12))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H35. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H36. % 51.19/51.39 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.39 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e10) (e13)) = (e10)) = ((e12) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H38. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H4e. % 51.19/51.39 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.39 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H4f zenon_H49). % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L16_ *) % 51.19/51.39 assert (zenon_L17_ : ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e13)) = (e13)) -> (~((e10) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H50 zenon_H51 zenon_H42. % 51.19/51.39 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.39 cut (((e13) = (e13)) = ((e10) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H42. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3e. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e11) (e13)) = (e10)) = ((e13) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H43. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H50. % 51.19/51.39 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H52 zenon_H51). % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L17_ *) % 51.19/51.39 assert (zenon_L18_ : (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e10))/\(((op1 (op1 (e11) (e11)) (op1 (e11) (e11))) = (e11))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e12))/\((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e13))))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H53 zenon_H51 zenon_H54. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H54. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e13)) = ((op1 (e13) (e13)) = (op1 (e11) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H5d. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H59. % 51.19/51.39 cut (((e13) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 51.19/51.39 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H5f. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (op1 (e11) (e13)) (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e13) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 51.19/51.39 cut (((e13) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H5e. apply sym_equal. exact zenon_H51. % 51.19/51.39 apply zenon_H5e. apply sym_equal. exact zenon_H51. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5e. apply sym_equal. exact zenon_H51. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L18_ *) % 51.19/51.39 assert (zenon_L19_ : (~((op1 (e10) (e10)) = (op1 (op1 (e12) (e13)) (op1 (e12) (e13))))) -> ((op1 (e12) (e13)) = (e10)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H61 zenon_H62. % 51.19/51.39 cut (((e10) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 51.19/51.39 cut (((e10) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H63. apply sym_equal. exact zenon_H62. % 51.19/51.39 apply zenon_H63. apply sym_equal. exact zenon_H62. % 51.19/51.39 (* end of lemma zenon_L19_ *) % 51.19/51.39 assert (zenon_L20_ : (((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e10))/\(((op1 (op1 (e12) (e11)) (op1 (e12) (e11))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H64 zenon_H65 zenon_H62 zenon_H66. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H68. zenon_intro zenon_H67. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 51.19/51.39 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e13)) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H65. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H6b. % 51.19/51.39 cut (((e13) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 51.19/51.39 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H6e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2f. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (op1 (e12) (e13)) (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L19_); trivial. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H6d. apply sym_equal. exact zenon_H66. % 51.19/51.39 (* end of lemma zenon_L20_ *) % 51.19/51.39 assert (zenon_L21_ : (~((op1 (e11) (e11)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H6f zenon_H19. % 51.19/51.39 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 51.19/51.39 cut (((e11) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H70 zenon_H19). % 51.19/51.39 exact (zenon_H70 zenon_H19). % 51.19/51.39 (* end of lemma zenon_L21_ *) % 51.19/51.39 assert (zenon_L22_ : (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e10))/\(((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e11))/\(((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H71 zenon_H72 zenon_H19 zenon_H51. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 51.19/51.39 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13)) = ((op1 (e11) (e11)) = (op1 (e11) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H72. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H77. % 51.19/51.39 cut (((e13) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 51.19/51.39 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H7a | zenon_intro zenon_H7b ]. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H79. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H7a. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L21_); trivial. % 51.19/51.39 apply zenon_H7b. apply refl_equal. % 51.19/51.39 apply zenon_H7b. apply refl_equal. % 51.19/51.39 apply zenon_H5e. apply sym_equal. exact zenon_H51. % 51.19/51.39 (* end of lemma zenon_L22_ *) % 51.19/51.39 assert (zenon_L23_ : ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H7c zenon_H22 zenon_H7d zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19 zenon_H51. % 51.19/51.39 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 51.19/51.39 cut (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e12)) = ((op1 (e10) (e10)) = (op1 (e12) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H7d. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H85. % 51.19/51.39 cut (((e12) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 51.19/51.39 cut (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H87. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2f. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (op1 (e10) (e12)) (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 51.19/51.39 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H89]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H89. apply sym_equal. exact zenon_H22. % 51.19/51.39 apply zenon_H89. apply sym_equal. exact zenon_H22. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H86. apply sym_equal. exact zenon_H7c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.39 apply (zenon_L18_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.39 apply (zenon_L20_); trivial. % 51.19/51.39 apply (zenon_L22_); trivial. % 51.19/51.39 (* end of lemma zenon_L23_ *) % 51.19/51.39 assert (zenon_L24_ : ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e13)) = (e10)) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H19 zenon_H8b zenon_H8c. % 51.19/51.39 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H8d | zenon_intro zenon_H3a ]. % 51.19/51.39 cut (((e11) = (e11)) = ((e10) = (e11))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H8c. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H8d. % 51.19/51.39 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.39 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e11) = (op1 (e13) (e13))) = ((e11) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H8e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H19. % 51.19/51.39 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 51.19/51.39 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 exact (zenon_H8f zenon_H8b). % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L24_ *) % 51.19/51.39 assert (zenon_L25_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H90 zenon_H35 zenon_H49 zenon_H42 zenon_H51 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H7d zenon_H22 zenon_H7c zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.39 apply (zenon_L16_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.39 apply (zenon_L17_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L23_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L25_ *) % 51.19/51.39 assert (zenon_L26_ : (~((op1 (e12) (e12)) = (op1 (op1 (e10) (e13)) (op1 (e10) (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H93 zenon_H49. % 51.19/51.39 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 51.19/51.39 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H94. apply sym_equal. exact zenon_H49. % 51.19/51.39 apply zenon_H94. apply sym_equal. exact zenon_H49. % 51.19/51.39 (* end of lemma zenon_L26_ *) % 51.19/51.39 assert (zenon_L27_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e11))/\(((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e12))/\((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H7f zenon_H95 zenon_H49 zenon_H96. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 51.19/51.39 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e12) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H95. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H84. % 51.19/51.39 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 51.19/51.39 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.19/51.39 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H98. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H99. % 51.19/51.39 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.19/51.39 cut (((op1 (e12) (e12)) = (op1 (op1 (e10) (e13)) (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L26_); trivial. % 51.19/51.39 apply zenon_H9a. apply refl_equal. % 51.19/51.39 apply zenon_H9a. apply refl_equal. % 51.19/51.39 apply zenon_H97. apply sym_equal. exact zenon_H96. % 51.19/51.39 (* end of lemma zenon_L27_ *) % 51.19/51.39 assert (zenon_L28_ : (~((op1 (e10) (e10)) = (op1 (op1 (e11) (e13)) (op1 (e11) (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H9b zenon_H50. % 51.19/51.39 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 51.19/51.39 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H9c. apply sym_equal. exact zenon_H50. % 51.19/51.39 apply zenon_H9c. apply sym_equal. exact zenon_H50. % 51.19/51.39 (* end of lemma zenon_L28_ *) % 51.19/51.39 assert (zenon_L29_ : (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e10))/\(((op1 (op1 (e11) (e11)) (op1 (e11) (e11))) = (e11))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e12))/\((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H53 zenon_H65 zenon_H50 zenon_H66. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 51.19/51.39 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e13)) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H65. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H59. % 51.19/51.39 cut (((e13) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 51.19/51.39 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H9d. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2f. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (op1 (e11) (e13)) (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L28_); trivial. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H6d. apply sym_equal. exact zenon_H66. % 51.19/51.39 (* end of lemma zenon_L29_ *) % 51.19/51.39 assert (zenon_L30_ : (((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e10))/\(((op1 (op1 (e12) (e11)) (op1 (e12) (e11))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e13))))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H64 zenon_H96 zenon_H9e. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H68. zenon_intro zenon_H67. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H9e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e13)) = ((op1 (e13) (e13)) = (op1 (e12) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H9f. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H6b. % 51.19/51.39 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 51.19/51.39 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Ha0. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (op1 (e12) (e13)) (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_Ha1]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 51.19/51.39 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H97. apply sym_equal. exact zenon_H96. % 51.19/51.39 apply zenon_H97. apply sym_equal. exact zenon_H96. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H97. apply sym_equal. exact zenon_H96. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L30_ *) % 51.19/51.39 assert (zenon_L31_ : (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e10))/\(((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e11))/\(((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e12)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H71 zenon_Ha2 zenon_H19 zenon_Ha3. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 51.19/51.39 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13)) = ((op1 (e11) (e11)) = (op1 (e11) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Ha2. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H77. % 51.19/51.39 cut (((e13) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 51.19/51.39 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H7a | zenon_intro zenon_H7b ]. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H79. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H7a. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H6f]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L21_); trivial. % 51.19/51.39 apply zenon_H7b. apply refl_equal. % 51.19/51.39 apply zenon_H7b. apply refl_equal. % 51.19/51.39 apply zenon_Ha4. apply sym_equal. exact zenon_Ha3. % 51.19/51.39 (* end of lemma zenon_L31_ *) % 51.19/51.39 assert (zenon_L32_ : ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e12)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H49 zenon_H95 zenon_H66 zenon_H50 zenon_H65 zenon_H9e zenon_H96 zenon_Ha2 zenon_H19 zenon_Ha3. % 51.19/51.39 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.39 apply (zenon_L27_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.39 apply (zenon_L29_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.39 apply (zenon_L30_); trivial. % 51.19/51.39 apply (zenon_L31_); trivial. % 51.19/51.39 (* end of lemma zenon_L32_ *) % 51.19/51.39 assert (zenon_L33_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e11)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H54 zenon_H19 zenon_Ha5. % 51.19/51.39 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H54. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H19. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e11) = (op1 (e11) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Ha6. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Ha7. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Ha9 zenon_Ha5). % 51.19/51.39 apply zenon_Ha8. apply refl_equal. % 51.19/51.39 apply zenon_Ha8. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L33_ *) % 51.19/51.39 assert (zenon_L34_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e11) (e13)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H2c zenon_Haa zenon_H1c zenon_Hab. % 51.19/51.39 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hab. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Ha7. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hac]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e11) (e13)) = (op1 (e10) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hac. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2c. % 51.19/51.39 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 51.19/51.39 cut (((e12) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e12) = (op1 (e11) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Had. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Ha7. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hae]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Hae zenon_Haa). % 51.19/51.39 apply zenon_Ha8. apply refl_equal. % 51.19/51.39 apply zenon_Ha8. apply refl_equal. % 51.19/51.39 apply (zenon_L6_); trivial. % 51.19/51.39 apply zenon_Ha8. apply refl_equal. % 51.19/51.39 apply zenon_Ha8. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L34_ *) % 51.19/51.39 assert (zenon_L35_ : (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_Haf zenon_H51 zenon_H96. % 51.19/51.39 cut (((op1 (e11) (e13)) = (e13)) = ((op1 (e11) (e13)) = (op1 (e12) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Haf. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H51. % 51.19/51.39 cut (((e13) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 51.19/51.39 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_Ha8. apply refl_equal. % 51.19/51.39 apply zenon_H97. apply sym_equal. exact zenon_H96. % 51.19/51.39 (* end of lemma zenon_L35_ *) % 51.19/51.39 assert (zenon_L36_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hb0 zenon_Ha3 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H19 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H96. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.19/51.39 apply (zenon_L32_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.19/51.39 apply (zenon_L33_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.19/51.39 apply (zenon_L34_); trivial. % 51.19/51.39 apply (zenon_L35_); trivial. % 51.19/51.39 (* end of lemma zenon_L36_ *) % 51.19/51.39 assert (zenon_L37_ : (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e13)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H3d zenon_H19 zenon_Hb3. % 51.19/51.39 cut (((e11) = (op1 (e13) (e13))) = ((e11) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H3d. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H19. % 51.19/51.39 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 51.19/51.39 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 exact (zenon_Hb4 zenon_Hb3). % 51.19/51.39 (* end of lemma zenon_L37_ *) % 51.19/51.39 assert (zenon_L38_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H8c zenon_H7c zenon_H22 zenon_H7d zenon_H72 zenon_H42 zenon_H35 zenon_H90 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.39 apply (zenon_L15_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.39 apply (zenon_L25_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_L36_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L38_ *) % 51.19/51.39 assert (zenon_L39_ : (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hb8 zenon_H1c zenon_Hb9 zenon_H19. % 51.19/51.39 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e10)) = (op1 (e13) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hb8. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H1c. % 51.19/51.39 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 51.19/51.39 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hbc ]. % 51.19/51.39 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e10) = (op1 (e13) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hba. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Hbb. % 51.19/51.39 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 51.19/51.39 cut (((op1 (e13) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Hbd zenon_Hb9). % 51.19/51.39 apply zenon_Hbc. apply refl_equal. % 51.19/51.39 apply zenon_Hbc. apply refl_equal. % 51.19/51.39 apply (zenon_L3_); trivial. % 51.19/51.39 (* end of lemma zenon_L39_ *) % 51.19/51.39 assert (zenon_L40_ : ((op1 (e13) (e11)) = (e10)) -> ((op1 (e13) (e11)) = (e13)) -> (~((e10) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hbe zenon_Hbf zenon_H42. % 51.19/51.39 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.39 cut (((e13) = (e13)) = ((e10) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H42. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3e. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e13) (e11)) = (e10)) = ((e13) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H43. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Hbe. % 51.19/51.39 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.39 cut (((op1 (e13) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Hc0 zenon_Hbf). % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L40_ *) % 51.19/51.39 assert (zenon_L41_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H1c zenon_Hc1 zenon_H19 zenon_Hc2. % 51.19/51.39 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc4 ]. % 51.19/51.39 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((op1 (e13) (e11)) = (op1 (e13) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hc2. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Hc3. % 51.19/51.39 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 51.19/51.39 cut (((op1 (e13) (e12)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e12)) = (op1 (e13) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hc5. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H1c. % 51.19/51.39 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 51.19/51.39 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc4 ]. % 51.19/51.39 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e10) = (op1 (e13) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hc6. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Hc3. % 51.19/51.39 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 51.19/51.39 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Hc7]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Hc7 zenon_Hc1). % 51.19/51.39 apply zenon_Hc4. apply refl_equal. % 51.19/51.39 apply zenon_Hc4. apply refl_equal. % 51.19/51.39 apply (zenon_L3_); trivial. % 51.19/51.39 apply zenon_Hc4. apply refl_equal. % 51.19/51.39 apply zenon_Hc4. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L41_ *) % 51.19/51.39 assert (zenon_L42_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hbf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.39 apply (zenon_L39_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.39 apply (zenon_L40_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L41_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L42_ *) % 51.19/51.39 assert (zenon_L43_ : (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hcb zenon_Ha3 zenon_Hcc. % 51.19/51.39 cut (((op1 (e11) (e12)) = (e13)) = ((op1 (e11) (e12)) = (op1 (e13) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hcb. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Ha3. % 51.19/51.39 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 51.19/51.39 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_Hce. apply refl_equal. % 51.19/51.39 apply zenon_Hcd. apply sym_equal. exact zenon_Hcc. % 51.19/51.39 (* end of lemma zenon_L43_ *) % 51.19/51.39 assert (zenon_L44_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H90 zenon_H35 zenon_H72 zenon_H7d zenon_H22 zenon_H7c zenon_H4b zenon_Hb5 zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.39 apply (zenon_L38_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.39 apply (zenon_L42_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_L43_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L44_ *) % 51.19/51.39 assert (zenon_L45_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e12) (e13)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H2c zenon_Hd2 zenon_H1c zenon_Hd3. % 51.19/51.39 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ]. % 51.19/51.39 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hd3. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Hd4. % 51.19/51.39 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 51.19/51.39 cut (((op1 (e12) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e12) (e13)) = (op1 (e10) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hd6. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2c. % 51.19/51.39 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 51.19/51.39 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ]. % 51.19/51.39 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e12) = (op1 (e12) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hd7. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Hd4. % 51.19/51.39 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 51.19/51.39 cut (((op1 (e12) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd8]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Hd8 zenon_Hd2). % 51.19/51.39 apply zenon_Hd5. apply refl_equal. % 51.19/51.39 apply zenon_Hd5. apply refl_equal. % 51.19/51.39 apply (zenon_L6_); trivial. % 51.19/51.39 apply zenon_Hd5. apply refl_equal. % 51.19/51.39 apply zenon_Hd5. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L45_ *) % 51.19/51.39 assert (zenon_L46_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e13) (e13)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H2c zenon_Hd9 zenon_H1c zenon_Hda. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hda. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e13) (e13)) = (op1 (e10) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hdb. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2c. % 51.19/51.39 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 51.19/51.39 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e12) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hdc. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Hdd zenon_Hd9). % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply (zenon_L6_); trivial. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L46_ *) % 51.19/51.39 assert (zenon_L47_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hde zenon_H35 zenon_H4e zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.19/51.39 apply (zenon_L16_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.19/51.39 apply (zenon_L34_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.19/51.39 apply (zenon_L45_); trivial. % 51.19/51.39 apply (zenon_L46_); trivial. % 51.19/51.39 (* end of lemma zenon_L47_ *) % 51.19/51.39 assert (zenon_L48_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e11))/\(((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e12))/\((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H7f zenon_He1 zenon_H49 zenon_Hcc. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 51.19/51.39 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_He1. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H84. % 51.19/51.39 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 51.19/51.39 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.19/51.39 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H98. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H99. % 51.19/51.39 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.19/51.39 cut (((op1 (e12) (e12)) = (op1 (op1 (e10) (e13)) (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L26_); trivial. % 51.19/51.39 apply zenon_H9a. apply refl_equal. % 51.19/51.39 apply zenon_H9a. apply refl_equal. % 51.19/51.39 apply zenon_Hcd. apply sym_equal. exact zenon_Hcc. % 51.19/51.39 (* end of lemma zenon_L48_ *) % 51.19/51.39 assert (zenon_L49_ : (((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e10))/\(((op1 (op1 (e12) (e11)) (op1 (e12) (e11))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H64 zenon_H7d zenon_H62 zenon_He2. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H68. zenon_intro zenon_H67. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H67). zenon_intro zenon_H6a. zenon_intro zenon_H69. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H69). zenon_intro zenon_H6c. zenon_intro zenon_H6b. % 51.19/51.39 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e13)) = ((op1 (e10) (e10)) = (op1 (e12) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H7d. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H6b. % 51.19/51.39 cut (((e13) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 51.19/51.39 cut (((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H6e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2f. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (op1 (e12) (e13)) (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L19_); trivial. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_He3. apply sym_equal. exact zenon_He2. % 51.19/51.39 (* end of lemma zenon_L49_ *) % 51.19/51.39 assert (zenon_L50_ : (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e10))/\(((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e11))/\(((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H71 zenon_Hcc zenon_H49 zenon_Hda. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hda. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e12)) = ((op1 (e13) (e13)) = (op1 (e10) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hdb. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H78. % 51.19/51.39 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 51.19/51.39 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_He4. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H5b. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (op1 (e13) (e12)) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 51.19/51.39 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_Hcd. apply sym_equal. exact zenon_Hcc. % 51.19/51.39 apply zenon_Hcd. apply sym_equal. exact zenon_Hcc. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H94. apply sym_equal. exact zenon_H49. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L50_ *) % 51.19/51.39 assert (zenon_L51_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H62 zenon_H7d zenon_Hcc zenon_H49 zenon_Hda. % 51.19/51.39 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.39 apply (zenon_L48_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.39 apply (zenon_L18_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.39 apply (zenon_L49_); trivial. % 51.19/51.39 apply (zenon_L50_); trivial. % 51.19/51.39 (* end of lemma zenon_L51_ *) % 51.19/51.39 assert (zenon_L52_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_Hcc zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.39 apply (zenon_L16_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.39 apply (zenon_L17_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L51_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L52_ *) % 51.19/51.39 assert (zenon_L53_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hcf zenon_H72 zenon_H65 zenon_H62 zenon_H22 zenon_H7c zenon_Hbe zenon_H8c zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.39 apply (zenon_L23_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.39 apply (zenon_L40_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_L52_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L53_ *) % 51.19/51.39 assert (zenon_L54_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hde zenon_H3d zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_Hbe zenon_H7c zenon_H22 zenon_H65 zenon_H72 zenon_Hcf zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.39 apply (zenon_L47_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.39 apply (zenon_L17_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L53_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L54_ *) % 51.19/51.39 assert (zenon_L55_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H72 zenon_H65 zenon_H22 zenon_H7c zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_Hde zenon_Hab zenon_Hd3 zenon_H2c zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.39 apply (zenon_L39_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.39 apply (zenon_L54_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L41_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L55_ *) % 51.19/51.39 assert (zenon_L56_ : ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((e10) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H22 zenon_He6 zenon_H42. % 51.19/51.39 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.39 cut (((e13) = (e13)) = ((e10) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H42. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3e. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e10) (e12)) = (e10)) = ((e13) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H43. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H22. % 51.19/51.39 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.39 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_He7 zenon_He6). % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L56_ *) % 51.19/51.39 assert (zenon_L57_ : ((op1 (e13) (e10)) = (e12)) -> ((op1 (e13) (e10)) = (e13)) -> (~((e12) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_He8 zenon_H66 zenon_H4b. % 51.19/51.39 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.39 cut (((e13) = (e13)) = ((e12) = (e13))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H4b. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H3e. % 51.19/51.39 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.39 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e13) (e10)) = (e12)) = ((e13) = (e12))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H4c. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_He8. % 51.19/51.39 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.39 cut (((op1 (e13) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_He9]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_He9 zenon_H66). % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 apply zenon_H17. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L57_ *) % 51.19/51.39 assert (zenon_L58_ : (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e10))/\(((op1 (op1 (e11) (e11)) (op1 (e11) (e11))) = (e11))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e12))/\((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H53 zenon_Hea zenon_H50 zenon_H41. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 51.19/51.39 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e13)) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hea. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H59. % 51.19/51.39 cut (((e13) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 51.19/51.39 cut (((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e10) (e10)) = (op1 (e10) (e10)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10))) = ((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H9d. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H2f. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 51.19/51.39 cut (((op1 (e10) (e10)) = (op1 (op1 (e11) (e13)) (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 51.19/51.39 congruence. % 51.19/51.39 apply (zenon_L28_); trivial. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_H30. apply refl_equal. % 51.19/51.39 apply zenon_Heb. apply sym_equal. exact zenon_H41. % 51.19/51.39 (* end of lemma zenon_L58_ *) % 51.19/51.39 assert (zenon_L59_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_He1 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_H96 zenon_Hcc zenon_H49 zenon_Hda. % 51.19/51.39 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.39 apply (zenon_L48_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.39 apply (zenon_L58_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.39 apply (zenon_L30_); trivial. % 51.19/51.39 apply (zenon_L50_); trivial. % 51.19/51.39 (* end of lemma zenon_L59_ *) % 51.19/51.39 assert (zenon_L60_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hcf zenon_H4b zenon_He8 zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hda zenon_H49 zenon_H96 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_He1 zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.39 apply (zenon_L57_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.39 apply (zenon_L42_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_L59_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L60_ *) % 51.19/51.39 assert (zenon_L61_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hb5 zenon_H8c zenon_He1 zenon_H54 zenon_He2 zenon_H7d zenon_Hcc zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H2c zenon_H1c zenon_Hab zenon_Hcf zenon_H4b zenon_He8 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H9e zenon_Hea zenon_H41 zenon_Hb0 zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.39 apply (zenon_L15_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.39 apply (zenon_L52_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.19/51.39 apply (zenon_L60_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.19/51.39 apply (zenon_L33_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.19/51.39 apply (zenon_L34_); trivial. % 51.19/51.39 apply (zenon_L52_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L61_ *) % 51.19/51.39 assert (zenon_L62_ : (((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 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hb0 zenon_H41 zenon_Hea zenon_H9e zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_He8 zenon_H4b zenon_Hcf zenon_Hab zenon_H1c zenon_H2c zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H8c zenon_Hb5 zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.39 apply (zenon_L57_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.39 apply (zenon_L42_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_L61_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L62_ *) % 51.19/51.39 assert (zenon_L63_ : (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e12)) = (e11)) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hec zenon_H19 zenon_Hed. % 51.19/51.39 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e12)) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hec. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H19. % 51.19/51.39 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.39 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_Hc3 | zenon_intro zenon_Hc4 ]. % 51.19/51.39 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e11) = (op1 (e13) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hee. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_Hc3. % 51.19/51.39 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hc4]. % 51.19/51.39 cut (((op1 (e13) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hef]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_Hef zenon_Hed). % 51.19/51.39 apply zenon_Hc4. apply refl_equal. % 51.19/51.39 apply zenon_Hc4. apply refl_equal. % 51.19/51.39 apply zenon_H5c. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L63_ *) % 51.19/51.39 assert (zenon_L64_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hf0 zenon_He8 zenon_Hf1. % 51.19/51.39 cut (((op1 (e13) (e10)) = (e12)) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hf0. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_He8. % 51.19/51.39 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 51.19/51.39 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_Hbc. apply refl_equal. % 51.19/51.39 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 51.19/51.39 (* end of lemma zenon_L64_ *) % 51.19/51.39 assert (zenon_L65_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hf3 zenon_Hc2 zenon_H1c zenon_H19 zenon_Hec zenon_He8 zenon_Hf0 zenon_Hcb zenon_Ha3. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hf4 ]. % 51.19/51.39 apply (zenon_L41_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hed | zenon_intro zenon_Hf5 ]. % 51.19/51.39 apply (zenon_L63_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcc ]. % 51.19/51.39 apply (zenon_L64_); trivial. % 51.19/51.39 apply (zenon_L43_); trivial. % 51.19/51.39 (* end of lemma zenon_L65_ *) % 51.19/51.39 assert (zenon_L66_ : (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> ((op1 (e11) (e13)) = (e10)) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hf6 zenon_H33 zenon_H50. % 51.19/51.39 cut (((op1 (e11) (e10)) = (e10)) = ((op1 (e11) (e10)) = (op1 (e11) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_Hf6. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H33. % 51.19/51.39 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 51.19/51.39 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_Hf7. apply refl_equal. % 51.19/51.39 apply zenon_H9c. apply sym_equal. exact zenon_H50. % 51.19/51.39 (* end of lemma zenon_L66_ *) % 51.19/51.39 assert (zenon_L67_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_Hbe zenon_Hda zenon_H49 zenon_H7d zenon_H62 zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.39 apply (zenon_L57_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.39 apply (zenon_L40_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_L51_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L67_ *) % 51.19/51.39 assert (zenon_L68_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H90 zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H33 zenon_Hf6 zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_Hbe zenon_H42 zenon_He8 zenon_H4b zenon_Hcf zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.39 apply (zenon_L47_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.39 apply (zenon_L66_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L67_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L68_ *) % 51.19/51.39 assert (zenon_L69_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_Hf6 zenon_H33 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.39 apply (zenon_L39_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.39 apply (zenon_L68_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L41_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L69_ *) % 51.19/51.39 assert (zenon_L70_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hf8 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_H46 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H3d zenon_Hf6 zenon_H33 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.39 apply (zenon_L62_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.39 apply (zenon_L13_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.39 apply (zenon_L65_); trivial. % 51.19/51.39 apply (zenon_L69_); trivial. % 51.19/51.39 (* end of lemma zenon_L70_ *) % 51.19/51.39 assert (zenon_L71_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hfb zenon_H3b zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H90 zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H33 zenon_Hf6 zenon_H3d zenon_He1 zenon_H54 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_H46 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_Hf8 zenon_He8 zenon_H4b. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.19/51.39 apply (zenon_L11_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.19/51.39 apply (zenon_L12_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.19/51.39 apply (zenon_L70_); trivial. % 51.19/51.39 apply (zenon_L57_); trivial. % 51.19/51.39 (* end of lemma zenon_L71_ *) % 51.19/51.39 assert (zenon_L72_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (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)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hfe zenon_H2b zenon_Ha2 zenon_H95 zenon_Haf zenon_H72 zenon_H65 zenon_Hff zenon_Hf8 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hda zenon_H7d zenon_H54 zenon_He1 zenon_H3d zenon_Hf6 zenon_H33 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c zenon_H3b zenon_Hfb zenon_H42 zenon_H22 zenon_H49 zenon_H4b. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.19/51.39 apply (zenon_L7_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.19/51.39 apply (zenon_L9_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.19/51.39 apply (zenon_L11_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.19/51.39 apply (zenon_L11_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.19/51.39 apply (zenon_L12_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.39 apply (zenon_L12_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.39 apply (zenon_L13_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.39 apply (zenon_L44_); trivial. % 51.19/51.39 apply (zenon_L55_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.39 apply (zenon_L12_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.39 apply (zenon_L13_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.39 apply (zenon_L38_); trivial. % 51.19/51.39 apply (zenon_L25_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.19/51.39 apply (zenon_L56_); trivial. % 51.19/51.39 apply (zenon_L15_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.19/51.39 apply (zenon_L11_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.19/51.39 apply (zenon_L71_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.19/51.39 apply (zenon_L56_); trivial. % 51.19/51.39 apply (zenon_L15_); trivial. % 51.19/51.39 (* end of lemma zenon_L72_ *) % 51.19/51.39 assert (zenon_L73_ : ((op1 (e10) (e11)) = (e11)) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H104 zenon_H3b zenon_H105. % 51.19/51.39 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 51.19/51.39 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((op1 (e10) (e10)) = (op1 (e10) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H105. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H1f. % 51.19/51.39 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 51.19/51.39 cut (((op1 (e10) (e11)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e10) (e11)) = (e11)) = ((op1 (e10) (e11)) = (op1 (e10) (e10)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H106. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H104. % 51.19/51.39 cut (((e11) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 51.19/51.39 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H20. apply refl_equal. % 51.19/51.39 apply zenon_H107. apply sym_equal. exact zenon_H3b. % 51.19/51.39 apply zenon_H20. apply refl_equal. % 51.19/51.39 apply zenon_H20. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L73_ *) % 51.19/51.39 assert (zenon_L74_ : ((op1 (e11) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H33 zenon_H108 zenon_H8c. % 51.19/51.39 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H8d | zenon_intro zenon_H3a ]. % 51.19/51.39 cut (((e11) = (e11)) = ((e10) = (e11))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H8c. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H8d. % 51.19/51.39 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.39 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e11) (e10)) = (e10)) = ((e11) = (e10))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H8e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H33. % 51.19/51.39 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.39 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H109 zenon_H108). % 51.19/51.39 apply zenon_H32. apply refl_equal. % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L74_ *) % 51.19/51.39 assert (zenon_L75_ : ((op1 (e12) (e10)) = (e11)) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> False). % 51.19/51.39 do 0 intro. intros zenon_H10a zenon_H7c zenon_H10b. % 51.19/51.39 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.19/51.39 cut (((e12) = (e12)) = ((e11) = (e12))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H10b. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H36. % 51.19/51.39 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.39 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((op1 (e12) (e10)) = (e11)) = ((e12) = (e11))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H10c. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H10a. % 51.19/51.39 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.39 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 51.19/51.39 congruence. % 51.19/51.39 exact (zenon_H10d zenon_H7c). % 51.19/51.39 apply zenon_H3a. apply refl_equal. % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 apply zenon_H37. apply refl_equal. % 51.19/51.39 (* end of lemma zenon_L75_ *) % 51.19/51.39 assert (zenon_L76_ : (((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e10))/\(((op1 (op1 (e12) (e11)) (op1 (e12) (e11))) = (e11))/\(((op1 (op1 (e12) (e12)) (op1 (e12) (e12))) = (e12))/\((op1 (op1 (e12) (e13)) (op1 (e12) (e13))) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H64 zenon_H10e zenon_H10a zenon_Hbe. % 51.19/51.39 apply (zenon_and_s _ _ zenon_H64). zenon_intro zenon_H68. zenon_intro zenon_H67. % 51.19/51.39 cut (((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (e10)) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H10e. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H68. % 51.19/51.39 cut (((e10) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 51.19/51.39 cut (((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 51.19/51.39 congruence. % 51.19/51.39 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H7a | zenon_intro zenon_H7b ]. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e12) (e10)) (op1 (e12) (e10))) = (op1 (e11) (e11)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H110. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.39 exact zenon_H7a. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 51.19/51.39 cut (((op1 (e11) (e11)) = (op1 (op1 (e12) (e10)) (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 51.19/51.39 congruence. % 51.19/51.39 cut (((e11) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 51.19/51.39 cut (((e11) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 51.19/51.39 congruence. % 51.19/51.39 apply zenon_H112. apply sym_equal. exact zenon_H10a. % 51.19/51.39 apply zenon_H112. apply sym_equal. exact zenon_H10a. % 51.19/51.39 apply zenon_H7b. apply refl_equal. % 51.19/51.39 apply zenon_H7b. apply refl_equal. % 51.19/51.39 apply zenon_H10f. apply sym_equal. exact zenon_Hbe. % 51.19/51.39 (* end of lemma zenon_L76_ *) % 51.19/51.39 assert (zenon_L77_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_He1 zenon_H54 zenon_H51 zenon_Hbe zenon_H10a zenon_H10e zenon_Hcc zenon_H49 zenon_Hda. % 51.19/51.39 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.39 apply (zenon_L48_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.39 apply (zenon_L18_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.39 apply (zenon_L76_); trivial. % 51.19/51.39 apply (zenon_L50_); trivial. % 51.19/51.39 (* end of lemma zenon_L77_ *) % 51.19/51.39 assert (zenon_L78_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hb0 zenon_H33 zenon_Hf6 zenon_H19 zenon_Hab zenon_H1c zenon_H2c zenon_He1 zenon_H54 zenon_Hbe zenon_H10a zenon_H10e zenon_Hcc zenon_H49 zenon_Hda. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.19/51.39 apply (zenon_L66_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.19/51.39 apply (zenon_L33_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.19/51.39 apply (zenon_L34_); trivial. % 51.19/51.39 apply (zenon_L77_); trivial. % 51.19/51.39 (* end of lemma zenon_L78_ *) % 51.19/51.39 assert (zenon_L79_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hcf zenon_H4b zenon_He8 zenon_H8c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hda zenon_H49 zenon_H10e zenon_H10a zenon_Hbe zenon_H54 zenon_He1 zenon_H2c zenon_H1c zenon_Hab zenon_Hf6 zenon_H33 zenon_Hb0 zenon_H3d zenon_H19. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.39 apply (zenon_L57_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.39 apply (zenon_L42_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.39 apply (zenon_L78_); trivial. % 51.19/51.39 apply (zenon_L37_); trivial. % 51.19/51.39 (* end of lemma zenon_L79_ *) % 51.19/51.39 assert (zenon_L80_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e10) = (e12))) -> (~((e11) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hfe zenon_H2b zenon_H35 zenon_H10b zenon_H3d zenon_Hb0 zenon_H33 zenon_Hf6 zenon_Hab zenon_H2c zenon_He1 zenon_H54 zenon_H10a zenon_H10e zenon_H49 zenon_Hda zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.19/51.39 apply (zenon_L7_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.19/51.39 apply (zenon_L9_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.19/51.39 apply (zenon_L75_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.39 apply (zenon_L39_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.39 apply (zenon_L79_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.39 apply (zenon_L41_); trivial. % 51.19/51.39 apply (zenon_L24_); trivial. % 51.19/51.39 (* end of lemma zenon_L80_ *) % 51.19/51.39 assert (zenon_L81_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((e11) = (e12))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.39 do 0 intro. intros zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_Hcf zenon_H4b zenon_H42 zenon_Hb8 zenon_Hc8 zenon_H10e zenon_H10a zenon_H54 zenon_He1 zenon_Hf6 zenon_H33 zenon_Hb0 zenon_H3d zenon_H10b zenon_H35 zenon_H2b zenon_Hfe zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.19/51.39 apply (zenon_L80_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.19/51.39 apply (zenon_L34_); trivial. % 51.19/51.39 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.19/51.39 apply (zenon_L45_); trivial. % 51.19/51.39 apply (zenon_L46_); trivial. % 51.19/51.39 (* end of lemma zenon_L81_ *) % 51.19/51.39 assert (zenon_L82_ : (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e10)) = (e11)) -> False). % 51.19/51.39 do 0 intro. intros zenon_H113 zenon_H19 zenon_H114. % 51.19/51.39 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))). % 51.19/51.39 intro zenon_D_pnotp. % 51.19/51.39 apply zenon_H113. % 51.19/51.39 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H19. % 51.19/51.40 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.40 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hbc ]. % 51.19/51.40 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e11) = (op1 (e13) (e10)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H115. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_Hbb. % 51.19/51.40 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 51.19/51.40 cut (((op1 (e13) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H116 zenon_H114). % 51.19/51.40 apply zenon_Hbc. apply refl_equal. % 51.19/51.40 apply zenon_Hbc. apply refl_equal. % 51.19/51.40 apply zenon_H5c. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L82_ *) % 51.19/51.40 assert (zenon_L83_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e10) = (e12))) -> (~((e11) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H117 zenon_H105 zenon_H104 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hfe zenon_H2b zenon_H35 zenon_H10b zenon_H3d zenon_Hb0 zenon_H33 zenon_Hf6 zenon_He1 zenon_H54 zenon_H10e zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_Hc2 zenon_H8c zenon_Hde zenon_H113 zenon_H19. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.19/51.40 apply (zenon_L73_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.19/51.40 apply (zenon_L74_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.19/51.40 apply (zenon_L81_); trivial. % 51.19/51.40 apply (zenon_L82_); trivial. % 51.19/51.40 (* end of lemma zenon_L83_ *) % 51.19/51.40 assert (zenon_L84_ : ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> (~((e10) = (e11))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H22 zenon_H11a zenon_H8c. % 51.19/51.40 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H8d | zenon_intro zenon_H3a ]. % 51.19/51.40 cut (((e11) = (e11)) = ((e10) = (e11))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H8c. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H8d. % 51.19/51.40 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.40 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (e10) (e12)) = (e10)) = ((e11) = (e10))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H8e. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H22. % 51.19/51.40 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.40 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H11b zenon_H11a). % 51.19/51.40 apply zenon_H32. apply refl_equal. % 51.19/51.40 apply zenon_H3a. apply refl_equal. % 51.19/51.40 apply zenon_H3a. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L84_ *) % 51.19/51.40 assert (zenon_L85_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e13)) = (e11)) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hda zenon_H19 zenon_H11c. % 51.19/51.40 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_Hda. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H19. % 51.19/51.40 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.19/51.40 cut (((e11) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H11e | zenon_intro zenon_H11f ]. % 51.19/51.40 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e11) = (op1 (e10) (e13)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H11d. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H11e. % 51.19/51.40 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 51.19/51.40 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H120 zenon_H11c). % 51.19/51.40 apply zenon_H11f. apply refl_equal. % 51.19/51.40 apply zenon_H11f. apply refl_equal. % 51.19/51.40 apply zenon_H5c. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L85_ *) % 51.19/51.40 assert (zenon_L86_ : ((op1 (e11) (e10)) = (e12)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e12) = (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H34 zenon_H41 zenon_H4b. % 51.19/51.40 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.40 cut (((e13) = (e13)) = ((e12) = (e13))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H4b. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H3e. % 51.19/51.40 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.40 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (e11) (e10)) = (e12)) = ((e13) = (e12))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H4c. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H34. % 51.19/51.40 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.40 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H44 zenon_H41). % 51.19/51.40 apply zenon_H37. apply refl_equal. % 51.19/51.40 apply zenon_H17. apply refl_equal. % 51.19/51.40 apply zenon_H17. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L86_ *) % 51.19/51.40 assert (zenon_L87_ : ((op1 (e12) (e10)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> (~((e10) = (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H121 zenon_He2 zenon_H42. % 51.19/51.40 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.19/51.40 cut (((e13) = (e13)) = ((e10) = (e13))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H42. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H3e. % 51.19/51.40 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.19/51.40 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (e12) (e10)) = (e10)) = ((e13) = (e10))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H43. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H121. % 51.19/51.40 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.40 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H122 zenon_He2). % 51.19/51.40 apply zenon_H32. apply refl_equal. % 51.19/51.40 apply zenon_H17. apply refl_equal. % 51.19/51.40 apply zenon_H17. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L87_ *) % 51.19/51.40 assert (zenon_L88_ : (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e10)) -> ((op1 (e12) (e13)) = (e10)) -> False). % 51.19/51.40 do 0 intro. intros zenon_H123 zenon_H121 zenon_H62. % 51.19/51.40 cut (((op1 (e12) (e10)) = (e10)) = ((op1 (e12) (e10)) = (op1 (e12) (e13)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H123. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H121. % 51.19/51.40 cut (((e10) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 51.19/51.40 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H124. apply refl_equal. % 51.19/51.40 apply zenon_H63. apply sym_equal. exact zenon_H62. % 51.19/51.40 (* end of lemma zenon_L88_ *) % 51.19/51.40 assert (zenon_L89_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H90 zenon_H35 zenon_H49 zenon_H42 zenon_H51 zenon_H121 zenon_H123 zenon_H19 zenon_H8c. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.40 apply (zenon_L16_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.40 apply (zenon_L17_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.40 apply (zenon_L88_); trivial. % 51.19/51.40 apply (zenon_L24_); trivial. % 51.19/51.40 (* end of lemma zenon_L89_ *) % 51.19/51.40 assert (zenon_L90_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_H19 zenon_H3d zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_H90 zenon_H35 zenon_H121 zenon_H123 zenon_H8c zenon_H4b zenon_Hb5 zenon_H50 zenon_H42. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.40 apply (zenon_L86_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.40 apply (zenon_L13_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.40 apply (zenon_L15_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.40 apply (zenon_L89_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.40 apply (zenon_L32_); trivial. % 51.19/51.40 apply (zenon_L37_); trivial. % 51.19/51.40 apply (zenon_L17_); trivial. % 51.19/51.40 (* end of lemma zenon_L90_ *) % 51.19/51.40 assert (zenon_L91_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hff zenon_H8c zenon_H19 zenon_H123 zenon_H121 zenon_Hf8 zenon_H34 zenon_H45 zenon_H3d zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H90 zenon_H35 zenon_Hb5 zenon_H3b zenon_Hfb zenon_H42 zenon_H22 zenon_H49 zenon_H4b. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.19/51.40 apply (zenon_L11_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.19/51.40 apply (zenon_L11_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.19/51.40 apply (zenon_L86_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.19/51.40 apply (zenon_L87_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.40 apply (zenon_L16_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.40 apply (zenon_L90_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.40 apply (zenon_L88_); trivial. % 51.19/51.40 apply (zenon_L24_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.19/51.40 apply (zenon_L56_); trivial. % 51.19/51.40 apply (zenon_L15_); trivial. % 51.19/51.40 (* end of lemma zenon_L91_ *) % 51.19/51.40 assert (zenon_L92_ : ((op1 (e12) (e10)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> (~((e10) = (e12))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H121 zenon_H7c zenon_H35. % 51.19/51.40 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.19/51.40 cut (((e12) = (e12)) = ((e10) = (e12))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H35. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H36. % 51.19/51.40 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.40 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (e12) (e10)) = (e10)) = ((e12) = (e10))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H38. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H121. % 51.19/51.40 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.40 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H10d zenon_H7c). % 51.19/51.40 apply zenon_H32. apply refl_equal. % 51.19/51.40 apply zenon_H37. apply refl_equal. % 51.19/51.40 apply zenon_H37. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L92_ *) % 51.19/51.40 assert (zenon_L93_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H42 zenon_Hda zenon_H49 zenon_Hcc zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_He1 zenon_H3d zenon_H19. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.40 apply (zenon_L15_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.40 apply (zenon_L17_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.40 apply (zenon_L59_); trivial. % 51.19/51.40 apply (zenon_L37_); trivial. % 51.19/51.40 (* end of lemma zenon_L93_ *) % 51.19/51.40 assert (zenon_L94_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hcf zenon_He8 zenon_Hbe zenon_He1 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_H42 zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.40 apply (zenon_L57_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.40 apply (zenon_L40_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.40 apply (zenon_L93_); trivial. % 51.19/51.40 apply (zenon_L37_); trivial. % 51.19/51.40 (* end of lemma zenon_L94_ *) % 51.19/51.40 assert (zenon_L95_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H90 zenon_H35 zenon_H3d zenon_Hb5 zenon_H4b zenon_H42 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_Hbe zenon_He8 zenon_Hcf zenon_H121 zenon_H123 zenon_H19 zenon_H8c. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.40 apply (zenon_L16_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.40 apply (zenon_L94_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.40 apply (zenon_L88_); trivial. % 51.19/51.40 apply (zenon_L24_); trivial. % 51.19/51.40 (* end of lemma zenon_L95_ *) % 51.19/51.40 assert (zenon_L96_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e10)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hde zenon_H8c zenon_H19 zenon_H123 zenon_H121 zenon_Hcf zenon_He8 zenon_Hbe zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_H3d zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.19/51.40 apply (zenon_L95_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.19/51.40 apply (zenon_L34_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.19/51.40 apply (zenon_L45_); trivial. % 51.19/51.40 apply (zenon_L46_); trivial. % 51.19/51.40 (* end of lemma zenon_L96_ *) % 51.19/51.40 assert (zenon_L97_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H3d zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_He8 zenon_Hcf zenon_H121 zenon_H123 zenon_Hde zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.40 apply (zenon_L39_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.40 apply (zenon_L96_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.40 apply (zenon_L41_); trivial. % 51.19/51.40 apply (zenon_L24_); trivial. % 51.19/51.40 (* end of lemma zenon_L97_ *) % 51.19/51.40 assert (zenon_L98_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> ((op1 (e12) (e10)) = (e10)) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hfb zenon_H3b zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hde zenon_H123 zenon_Hcf zenon_He1 zenon_Hea zenon_H9e zenon_Hb5 zenon_H3d zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H42 zenon_H121 zenon_He8 zenon_H4b. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.19/51.40 apply (zenon_L11_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.19/51.40 apply (zenon_L97_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.19/51.40 apply (zenon_L87_); trivial. % 51.19/51.40 apply (zenon_L57_); trivial. % 51.19/51.40 (* end of lemma zenon_L98_ *) % 51.19/51.40 assert (zenon_L99_ : ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e10)) = (e12)) -> (~((e11) = (e12))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H108 zenon_H34 zenon_H10b. % 51.19/51.40 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.19/51.40 cut (((e12) = (e12)) = ((e11) = (e12))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H10b. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H36. % 51.19/51.40 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.40 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (e11) (e10)) = (e11)) = ((e12) = (e11))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H10c. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H108. % 51.19/51.40 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.40 cut (((op1 (e11) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H39 zenon_H34). % 51.19/51.40 apply zenon_H3a. apply refl_equal. % 51.19/51.40 apply zenon_H37. apply refl_equal. % 51.19/51.40 apply zenon_H37. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L99_ *) % 51.19/51.40 assert (zenon_L100_ : (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> False). % 51.19/51.40 do 0 intro. intros zenon_H125 zenon_H22 zenon_H126. % 51.19/51.40 cut (((op1 (e10) (e12)) = (e10)) = ((op1 (e10) (e12)) = (op1 (e11) (e12)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H125. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H22. % 51.19/51.40 cut (((e10) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 51.19/51.40 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H26. apply refl_equal. % 51.19/51.40 apply zenon_H127. apply sym_equal. exact zenon_H126. % 51.19/51.40 (* end of lemma zenon_L100_ *) % 51.19/51.40 assert (zenon_L101_ : (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False). % 51.19/51.40 do 0 intro. intros zenon_H128 zenon_H108 zenon_H129. % 51.19/51.40 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H128. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H108. % 51.19/51.40 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 51.19/51.40 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_Hf7. apply refl_equal. % 51.19/51.40 apply zenon_H12a. apply sym_equal. exact zenon_H129. % 51.19/51.40 (* end of lemma zenon_L101_ *) % 51.19/51.40 assert (zenon_L102_ : (((op1 (op1 (e11) (e10)) (op1 (e11) (e10))) = (e10))/\(((op1 (op1 (e11) (e11)) (op1 (e11) (e11))) = (e11))/\(((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e12))/\((op1 (op1 (e11) (e13)) (op1 (e11) (e13))) = (e13))))) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H53 zenon_H12b zenon_H12c. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H53). zenon_intro zenon_H56. zenon_intro zenon_H55. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H55). zenon_intro zenon_H58. zenon_intro zenon_H57. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H57). zenon_intro zenon_H5a. zenon_intro zenon_H59. % 51.19/51.40 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.19/51.40 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e11) (e12)) = (op1 (e12) (e12)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H12c. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H99. % 51.19/51.40 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.19/51.40 cut (((op1 (e12) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (e12)) = ((op1 (e12) (e12)) = (op1 (e11) (e12)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H12d. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H5a. % 51.19/51.40 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 51.19/51.40 cut (((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.19/51.40 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e11) (e12)) (op1 (e11) (e12))) = (op1 (e12) (e12)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H12f. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H99. % 51.19/51.40 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.19/51.40 cut (((op1 (e12) (e12)) = (op1 (op1 (e11) (e12)) (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 51.19/51.40 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H12e. apply sym_equal. exact zenon_H12b. % 51.19/51.40 apply zenon_H12e. apply sym_equal. exact zenon_H12b. % 51.19/51.40 apply zenon_H9a. apply refl_equal. % 51.19/51.40 apply zenon_H9a. apply refl_equal. % 51.19/51.40 apply zenon_H12e. apply sym_equal. exact zenon_H12b. % 51.19/51.40 apply zenon_H9a. apply refl_equal. % 51.19/51.40 apply zenon_H9a. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L102_ *) % 51.19/51.40 assert (zenon_L103_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_He1 zenon_H12c zenon_H12b zenon_H9e zenon_H96 zenon_Hcc zenon_H49 zenon_Hda. % 51.19/51.40 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.40 apply (zenon_L48_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.40 apply (zenon_L102_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.40 apply (zenon_L30_); trivial. % 51.19/51.40 apply (zenon_L50_); trivial. % 51.19/51.40 (* end of lemma zenon_L103_ *) % 51.19/51.40 assert (zenon_L104_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hf3 zenon_Hc2 zenon_H1c zenon_H19 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H12b zenon_H9e zenon_H96 zenon_H49 zenon_Hda. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hf3); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hf4 ]. % 51.19/51.40 apply (zenon_L41_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hf4); [ zenon_intro zenon_Hed | zenon_intro zenon_Hf5 ]. % 51.19/51.40 apply (zenon_L63_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hf5); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hcc ]. % 51.19/51.40 apply (zenon_L64_); trivial. % 51.19/51.40 apply (zenon_L103_); trivial. % 51.19/51.40 (* end of lemma zenon_L104_ *) % 51.19/51.40 assert (zenon_L105_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H42 zenon_H50 zenon_Hda zenon_H49 zenon_H9e zenon_H12b zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_H1c zenon_Hc2 zenon_Hf3 zenon_H3d zenon_H19. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.40 apply (zenon_L15_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.40 apply (zenon_L17_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.40 apply (zenon_L104_); trivial. % 51.19/51.40 apply (zenon_L37_); trivial. % 51.19/51.40 (* end of lemma zenon_L105_ *) % 51.19/51.40 assert (zenon_L106_ : (((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) (e10)) = (op1 (e11) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H131 zenon_H22 zenon_H125 zenon_H108 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H50 zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_H1c zenon_H19 zenon_Hec zenon_He8 zenon_Hf0 zenon_Hcb. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H126 | zenon_intro zenon_H132 ]. % 51.19/51.40 apply (zenon_L100_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H129 | zenon_intro zenon_H133 ]. % 51.19/51.40 apply (zenon_L101_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H12b | zenon_intro zenon_Ha3 ]. % 51.19/51.40 apply (zenon_L105_); trivial. % 51.19/51.40 apply (zenon_L65_); trivial. % 51.19/51.40 (* end of lemma zenon_L106_ *) % 51.19/51.40 assert (zenon_L107_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((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))))) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.40 do 0 intro. intros zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_Hcb zenon_Hf0 zenon_Hec zenon_H1c zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H108 zenon_H125 zenon_H22 zenon_H131 zenon_H121 zenon_H123 zenon_H19 zenon_H8c. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.19/51.40 apply (zenon_L7_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.19/51.40 apply (zenon_L99_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.19/51.40 apply (zenon_L92_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.40 apply (zenon_L47_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.40 apply (zenon_L106_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.40 apply (zenon_L88_); trivial. % 51.19/51.40 apply (zenon_L24_); trivial. % 51.19/51.40 (* end of lemma zenon_L107_ *) % 51.19/51.40 assert (zenon_L108_ : ((op1 (e12) (e10)) = (e10)) -> ((op1 (e12) (e10)) = (e11)) -> (~((e10) = (e11))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H121 zenon_H10a zenon_H8c. % 51.19/51.40 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H8d | zenon_intro zenon_H3a ]. % 51.19/51.40 cut (((e11) = (e11)) = ((e10) = (e11))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H8c. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H8d. % 51.19/51.40 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.19/51.40 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (e12) (e10)) = (e10)) = ((e11) = (e10))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H8e. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H121. % 51.19/51.40 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.40 cut (((op1 (e12) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H134 zenon_H10a). % 51.19/51.40 apply zenon_H32. apply refl_equal. % 51.19/51.40 apply zenon_H3a. apply refl_equal. % 51.19/51.40 apply zenon_H3a. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L108_ *) % 51.19/51.40 assert (zenon_L109_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e10)) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_Hda zenon_H22 zenon_H8c zenon_H117 zenon_H105 zenon_H2c zenon_Hd3 zenon_Hab zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_H35 zenon_Hde zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H1c zenon_H19. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H135); [ zenon_intro zenon_H23 | zenon_intro zenon_H137 ]. % 51.19/51.40 apply (zenon_L5_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H137); [ zenon_intro zenon_H33 | zenon_intro zenon_H138 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.19/51.40 apply (zenon_L72_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.19/51.40 apply (zenon_L34_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.19/51.40 apply (zenon_L45_); trivial. % 51.19/51.40 apply (zenon_L46_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.19/51.40 apply (zenon_L83_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.19/51.40 apply (zenon_L84_); trivial. % 51.19/51.40 apply (zenon_L85_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H121 | zenon_intro zenon_Hb9 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.19/51.40 apply (zenon_L7_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.19/51.40 apply (zenon_L91_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.19/51.40 apply (zenon_L34_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.19/51.40 apply (zenon_L45_); trivial. % 51.19/51.40 apply (zenon_L46_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.19/51.40 apply (zenon_L92_); trivial. % 51.19/51.40 apply (zenon_L98_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.19/51.40 apply (zenon_L73_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.19/51.40 apply (zenon_L107_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.19/51.40 apply (zenon_L34_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.19/51.40 apply (zenon_L45_); trivial. % 51.19/51.40 apply (zenon_L46_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.19/51.40 apply (zenon_L108_); trivial. % 51.19/51.40 apply (zenon_L82_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.19/51.40 apply (zenon_L84_); trivial. % 51.19/51.40 apply (zenon_L85_); trivial. % 51.19/51.40 apply (zenon_L39_); trivial. % 51.19/51.40 (* end of lemma zenon_L109_ *) % 51.19/51.40 assert (zenon_L110_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H13b zenon_H14 zenon_H13 zenon_H13c zenon_H13d zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.19/51.40 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H13d. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H13. % 51.19/51.40 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H13f]. % 51.19/51.40 cut (((h4 (e10)) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [ zenon_intro zenon_H141 | zenon_intro zenon_H142 ]. % 51.19/51.40 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10)))) = ((h4 (e10)) = (h4 (op1 (e10) (e10))))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H140. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H141. % 51.19/51.40 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 51.19/51.40 cut (((h4 (op1 (e10) (e10))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op1 (e10) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H144 zenon_H23). % 51.19/51.40 apply zenon_H142. apply refl_equal. % 51.19/51.40 apply zenon_H142. apply refl_equal. % 51.19/51.40 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 51.19/51.40 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e10))))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H13f. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H145. % 51.19/51.40 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 51.19/51.40 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (h4 (e10)) (h4 (e10))) = (op2 (e23) (op2 (e23) (e23))))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H147. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H13c. % 51.19/51.40 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 51.19/51.40 cut (((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H145 | zenon_intro zenon_H146 ]. % 51.19/51.40 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H149. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H145. % 51.19/51.40 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 51.19/51.40 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 51.19/51.40 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 51.19/51.40 congruence. % 51.19/51.40 apply (zenon_L1_); trivial. % 51.19/51.40 apply (zenon_L1_); trivial. % 51.19/51.40 apply zenon_H146. apply refl_equal. % 51.19/51.40 apply zenon_H146. apply refl_equal. % 51.19/51.40 exact (zenon_H148 zenon_H14). % 51.19/51.40 apply zenon_H146. apply refl_equal. % 51.19/51.40 apply zenon_H146. apply refl_equal. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.19/51.40 apply (zenon_L4_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.19/51.40 apply (zenon_L109_); trivial. % 51.19/51.40 apply (zenon_L47_); trivial. % 51.19/51.40 (* end of lemma zenon_L110_ *) % 51.19/51.40 assert (zenon_L111_ : (~((e23) = (e23))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H14c. % 51.19/51.40 apply zenon_H14c. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L111_ *) % 51.19/51.40 assert (zenon_L112_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H14d zenon_H14e. % 51.19/51.40 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 51.19/51.40 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H14c. apply refl_equal. % 51.19/51.40 apply zenon_H14f. apply sym_equal. exact zenon_H14e. % 51.19/51.40 (* end of lemma zenon_L112_ *) % 51.19/51.40 assert (zenon_L113_ : (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H150 zenon_H14 zenon_H151 zenon_H14e. % 51.19/51.40 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e20) (e21)) = (op2 (e23) (e21)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H150. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H14. % 51.19/51.40 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 51.19/51.40 cut (((e20) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H153 | zenon_intro zenon_H154 ]. % 51.19/51.40 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e20) = (op2 (e20) (e21)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H152. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H153. % 51.19/51.40 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 51.19/51.40 cut (((op2 (e20) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H155 zenon_H151). % 51.19/51.40 apply zenon_H154. apply refl_equal. % 51.19/51.40 apply zenon_H154. apply refl_equal. % 51.19/51.40 apply (zenon_L112_); trivial. % 51.19/51.40 (* end of lemma zenon_L113_ *) % 51.19/51.40 assert (zenon_L114_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H156 zenon_H13c zenon_H157. % 51.19/51.40 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H158 | zenon_intro zenon_H159 ]. % 51.19/51.40 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((op2 (e20) (e20)) = (op2 (e20) (e22)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H157. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H158. % 51.19/51.40 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 51.19/51.40 cut (((op2 (e20) (e22)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (e20) (e22)) = (op2 (e20) (e20)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H15a. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H156. % 51.19/51.40 cut (((e20) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 51.19/51.40 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H159. apply refl_equal. % 51.19/51.40 apply zenon_H15b. apply sym_equal. exact zenon_H13c. % 51.19/51.40 apply zenon_H159. apply refl_equal. % 51.19/51.40 apply zenon_H159. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L114_ *) % 51.19/51.40 assert (zenon_L115_ : (~((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H15c zenon_H14. % 51.19/51.40 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.40 cut (((op2 (e23) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H15. apply sym_equal. exact zenon_H14. % 51.19/51.40 apply zenon_H14c. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L115_ *) % 51.19/51.40 assert (zenon_L116_ : (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e20)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H15d zenon_H15e zenon_H15f zenon_H14. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e20) (e20)) = (op2 (e20) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H15d. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 51.19/51.40 cut (((e22) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 51.19/51.40 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((e22) = (op2 (e20) (e20)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H160. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H161. % 51.19/51.40 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 51.19/51.40 cut (((op2 (e20) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H163 zenon_H15f). % 51.19/51.40 apply zenon_H162. apply refl_equal. % 51.19/51.40 apply zenon_H162. apply refl_equal. % 51.19/51.40 apply (zenon_L115_); trivial. % 51.19/51.40 (* end of lemma zenon_L116_ *) % 51.19/51.40 assert (zenon_L117_ : (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e21)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H164 zenon_H15e zenon_H165 zenon_H14. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e20) (e21)) = (op2 (e20) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H164. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 51.19/51.40 cut (((e22) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H166]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H153 | zenon_intro zenon_H154 ]. % 51.19/51.40 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e22) = (op2 (e20) (e21)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H166. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H153. % 51.19/51.40 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 51.19/51.40 cut (((op2 (e20) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H167 zenon_H165). % 51.19/51.40 apply zenon_H154. apply refl_equal. % 51.19/51.40 apply zenon_H154. apply refl_equal. % 51.19/51.40 apply (zenon_L115_); trivial. % 51.19/51.40 (* end of lemma zenon_L117_ *) % 51.19/51.40 assert (zenon_L118_ : (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e22)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H168 zenon_H15e zenon_H169 zenon_H14. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e20) (e22)) = (op2 (e20) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H168. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 51.19/51.40 cut (((e22) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H158 | zenon_intro zenon_H159 ]. % 51.19/51.40 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((e22) = (op2 (e20) (e22)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H16a. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H158. % 51.19/51.40 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 51.19/51.40 cut (((op2 (e20) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H16b zenon_H169). % 51.19/51.40 apply zenon_H159. apply refl_equal. % 51.19/51.40 apply zenon_H159. apply refl_equal. % 51.19/51.40 apply (zenon_L115_); trivial. % 51.19/51.40 (* end of lemma zenon_L118_ *) % 51.19/51.40 assert (zenon_L119_ : (~((e20) = (e20))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H16c. % 51.19/51.40 apply zenon_H16c. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L119_ *) % 51.19/51.40 assert (zenon_L120_ : ((op2 (e21) (e20)) = (e20)) -> ((op2 (e21) (e20)) = (e22)) -> (~((e20) = (e22))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H16d zenon_H16e zenon_H16f. % 51.19/51.40 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H170 | zenon_intro zenon_H171 ]. % 51.19/51.40 cut (((e22) = (e22)) = ((e20) = (e22))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H16f. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H170. % 51.19/51.40 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.19/51.40 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op2 (e21) (e20)) = (e20)) = ((e22) = (e20))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H172. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H16d. % 51.19/51.40 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.40 cut (((op2 (e21) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H173]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H173 zenon_H16e). % 51.19/51.40 apply zenon_H16c. apply refl_equal. % 51.19/51.40 apply zenon_H171. apply refl_equal. % 51.19/51.40 apply zenon_H171. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L120_ *) % 51.19/51.40 assert (zenon_L121_ : (~((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e23)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> False). % 51.19/51.40 do 0 intro. intros zenon_H174 zenon_H175 zenon_H14 zenon_H176. % 51.19/51.40 cut (((op2 (e20) (e23)) = (e22)) = ((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e22) (e20)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H174. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H175. % 51.19/51.40 cut (((e22) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 51.19/51.40 cut (((op2 (e20) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [ zenon_intro zenon_H179 | zenon_intro zenon_H17a ]. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e20) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H178. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H179. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 51.19/51.40 congruence. % 51.19/51.40 apply (zenon_L115_); trivial. % 51.19/51.40 apply zenon_H17a. apply refl_equal. % 51.19/51.40 apply zenon_H17a. apply refl_equal. % 51.19/51.40 apply zenon_H177. apply sym_equal. exact zenon_H176. % 51.19/51.40 (* end of lemma zenon_L121_ *) % 51.19/51.40 assert (zenon_L122_ : (~((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e21) (e21)) = (e22)) -> False). % 51.19/51.40 do 0 intro. intros zenon_H17b zenon_H14 zenon_H176 zenon_H175 zenon_H17c. % 51.19/51.40 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e21)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H17b. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H176. % 51.19/51.40 cut (((e22) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 51.19/51.40 cut (((op2 (e22) (e20)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [ zenon_intro zenon_H179 | zenon_intro zenon_H17a ]. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e22) (e20)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H17e. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H179. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 51.19/51.40 congruence. % 51.19/51.40 apply (zenon_L121_); trivial. % 51.19/51.40 apply zenon_H17a. apply refl_equal. % 51.19/51.40 apply zenon_H17a. apply refl_equal. % 51.19/51.40 apply zenon_H17d. apply sym_equal. exact zenon_H17c. % 51.19/51.40 (* end of lemma zenon_L122_ *) % 51.19/51.40 assert (zenon_L123_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e21) (e22)) = (e22)) -> ((op2 (e21) (e21)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H15e zenon_H17f zenon_H17c zenon_H14 zenon_H176 zenon_H175 zenon_H180. % 51.19/51.40 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H181 | zenon_intro zenon_H182 ]. % 51.19/51.40 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((op2 (e21) (e21)) = (op2 (e21) (e22)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H180. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H181. % 51.19/51.40 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 51.19/51.40 cut (((op2 (e21) (e22)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e21) (e22)) = (op2 (e21) (e21)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H183. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 51.19/51.40 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H181 | zenon_intro zenon_H182 ]. % 51.19/51.40 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e22) = (op2 (e21) (e22)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H184. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H181. % 51.19/51.40 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 51.19/51.40 cut (((op2 (e21) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H185 zenon_H17f). % 51.19/51.40 apply zenon_H182. apply refl_equal. % 51.19/51.40 apply zenon_H182. apply refl_equal. % 51.19/51.40 apply (zenon_L122_); trivial. % 51.19/51.40 apply zenon_H182. apply refl_equal. % 51.19/51.40 apply zenon_H182. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L123_ *) % 51.19/51.40 assert (zenon_L124_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e21) (e23)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H15e zenon_H186 zenon_H14 zenon_H187. % 51.19/51.40 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 51.19/51.40 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H187. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H188. % 51.19/51.40 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 51.19/51.40 cut (((op2 (e21) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e21) (e23)) = (op2 (e20) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H18a. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 51.19/51.40 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H18b]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 51.19/51.40 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e22) = (op2 (e21) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H18b. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H188. % 51.19/51.40 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 51.19/51.40 cut (((op2 (e21) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H18c]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H18c zenon_H186). % 51.19/51.40 apply zenon_H189. apply refl_equal. % 51.19/51.40 apply zenon_H189. apply refl_equal. % 51.19/51.40 apply (zenon_L115_); trivial. % 51.19/51.40 apply zenon_H189. apply refl_equal. % 51.19/51.40 apply zenon_H189. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L124_ *) % 51.19/51.40 assert (zenon_L125_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e23)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H15e zenon_H18d zenon_H14 zenon_H18e. % 51.19/51.40 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H18f | zenon_intro zenon_H190 ]. % 51.19/51.40 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H18e. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H18f. % 51.19/51.40 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 51.19/51.40 cut (((op2 (e22) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e22) (e23)) = (op2 (e20) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H191. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 51.19/51.40 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H18f | zenon_intro zenon_H190 ]. % 51.19/51.40 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e22) = (op2 (e22) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H192. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H18f. % 51.19/51.40 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 51.19/51.40 cut (((op2 (e22) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H193 zenon_H18d). % 51.19/51.40 apply zenon_H190. apply refl_equal. % 51.19/51.40 apply zenon_H190. apply refl_equal. % 51.19/51.40 apply (zenon_L115_); trivial. % 51.19/51.40 apply zenon_H190. apply refl_equal. % 51.19/51.40 apply zenon_H190. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L125_ *) % 51.19/51.40 assert (zenon_L126_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e23) (e23)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H15e zenon_H194 zenon_H14 zenon_H195. % 51.19/51.40 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.40 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H195. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H196. % 51.19/51.40 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.40 cut (((op2 (e23) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e23) (e23)) = (op2 (e20) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H198. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 51.19/51.40 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.40 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((e22) = (op2 (e23) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H199. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H196. % 51.19/51.40 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.40 cut (((op2 (e23) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H19a zenon_H194). % 51.19/51.40 apply zenon_H197. apply refl_equal. % 51.19/51.40 apply zenon_H197. apply refl_equal. % 51.19/51.40 apply (zenon_L115_); trivial. % 51.19/51.40 apply zenon_H197. apply refl_equal. % 51.19/51.40 apply zenon_H197. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L126_ *) % 51.19/51.40 assert (zenon_L127_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e21) (e21)) = (e22)) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H19b zenon_H180 zenon_H176 zenon_H17c zenon_H17f zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.19/51.40 apply (zenon_L123_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.19/51.40 apply (zenon_L124_); trivial. % 51.19/51.40 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.19/51.40 apply (zenon_L125_); trivial. % 51.19/51.40 apply (zenon_L126_); trivial. % 51.19/51.40 (* end of lemma zenon_L127_ *) % 51.19/51.40 assert (zenon_L128_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e20)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H15e zenon_H19e zenon_H175 zenon_H176 zenon_H14 zenon_H19f. % 51.19/51.40 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.40 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e22) (e20)) = (op2 (e22) (e22)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H19f. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H1a0. % 51.19/51.40 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.40 cut (((op2 (e22) (e22)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1a2]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e22) (e22)) = (op2 (e22) (e20)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H1a2. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H15e. % 51.19/51.40 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 51.19/51.40 cut (((e22) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a3]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.40 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e22) = (op2 (e22) (e22)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H1a3. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H1a0. % 51.19/51.40 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.40 cut (((op2 (e22) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1a4]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H1a4 zenon_H19e). % 51.19/51.40 apply zenon_H1a1. apply refl_equal. % 51.19/51.40 apply zenon_H1a1. apply refl_equal. % 51.19/51.40 apply (zenon_L121_); trivial. % 51.19/51.40 apply zenon_H1a1. apply refl_equal. % 51.19/51.40 apply zenon_H1a1. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L128_ *) % 51.19/51.40 assert (zenon_L129_ : ((op2 (e20) (e23)) = (e20)) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e22))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H1a5 zenon_H175 zenon_H16f. % 51.19/51.40 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H170 | zenon_intro zenon_H171 ]. % 51.19/51.40 cut (((e22) = (e22)) = ((e20) = (e22))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H16f. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H170. % 51.19/51.40 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.19/51.40 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op2 (e20) (e23)) = (e20)) = ((e22) = (e20))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H172. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H1a5. % 51.19/51.40 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.40 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1a6]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H1a6 zenon_H175). % 51.19/51.40 apply zenon_H16c. apply refl_equal. % 51.19/51.40 apply zenon_H171. apply refl_equal. % 51.19/51.40 apply zenon_H171. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L129_ *) % 51.19/51.40 assert (zenon_L130_ : (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> ((op2 (e21) (e23)) = (e20)) -> False). % 51.19/51.40 do 0 intro. intros zenon_H1a7 zenon_H16d zenon_H1a8. % 51.19/51.40 cut (((op2 (e21) (e20)) = (e20)) = ((op2 (e21) (e20)) = (op2 (e21) (e23)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H1a7. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H16d. % 51.19/51.40 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 51.19/51.40 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H1aa. apply refl_equal. % 51.19/51.40 apply zenon_H1a9. apply sym_equal. exact zenon_H1a8. % 51.19/51.40 (* end of lemma zenon_L130_ *) % 51.19/51.40 assert (zenon_L131_ : (~((e22) = (e22))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H171. % 51.19/51.40 apply zenon_H171. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L131_ *) % 51.19/51.40 assert (zenon_L132_ : ((op2 (e20) (e23)) = (e22)) -> ((op2 (e20) (e23)) = (e23)) -> (~((e22) = (e23))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H175 zenon_H1ab zenon_H1ac. % 51.19/51.40 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.40 cut (((e23) = (e23)) = ((e22) = (e23))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H1ac. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H1ad. % 51.19/51.40 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.40 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((op2 (e20) (e23)) = (e22)) = ((e23) = (e22))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H1ae. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H175. % 51.19/51.40 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.19/51.40 cut (((op2 (e20) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 51.19/51.40 congruence. % 51.19/51.40 exact (zenon_H1af zenon_H1ab). % 51.19/51.40 apply zenon_H171. apply refl_equal. % 51.19/51.40 apply zenon_H14c. apply refl_equal. % 51.19/51.40 apply zenon_H14c. apply refl_equal. % 51.19/51.40 (* end of lemma zenon_L132_ *) % 51.19/51.40 assert (zenon_L133_ : (((op2 (op2 (e20) (e20)) (op2 (e20) (e20))) = (e20))/\(((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e21))/\(((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e22))/\((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e22) (e20)) = (e22)) -> False). % 51.19/51.40 do 0 intro. intros zenon_H1b0 zenon_H1b1 zenon_H156 zenon_H176. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_H1b3. zenon_intro zenon_H1b2. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b5. zenon_intro zenon_H1b4. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H1b7. zenon_intro zenon_H1b6. % 51.19/51.40 cut (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e22)) = ((op2 (e20) (e20)) = (op2 (e22) (e20)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H1b1. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H1b7. % 51.19/51.40 cut (((e22) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 51.19/51.40 cut (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 51.19/51.40 congruence. % 51.19/51.40 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 51.19/51.40 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (op2 (e20) (e20)))). % 51.19/51.40 intro zenon_D_pnotp. % 51.19/51.40 apply zenon_H1b8. % 51.19/51.40 rewrite <- zenon_D_pnotp. % 51.19/51.40 exact zenon_H161. % 51.19/51.40 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 51.19/51.40 cut (((op2 (e20) (e20)) = (op2 (op2 (e20) (e22)) (op2 (e20) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 51.19/51.40 congruence. % 51.19/51.40 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 51.19/51.40 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 51.19/51.40 congruence. % 51.19/51.40 apply zenon_H1ba. apply sym_equal. exact zenon_H156. % 51.19/51.40 apply zenon_H1ba. apply sym_equal. exact zenon_H156. % 51.19/51.40 apply zenon_H162. apply refl_equal. % 51.19/51.40 apply zenon_H162. apply refl_equal. % 51.19/51.40 apply zenon_H177. apply sym_equal. exact zenon_H176. % 51.19/51.40 (* end of lemma zenon_L133_ *) % 51.19/51.40 assert (zenon_L134_ : (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e20))/\(((op2 (op2 (e21) (e21)) (op2 (e21) (e21))) = (e21))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e22))/\((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e23))))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.40 do 0 intro. intros zenon_H1bb zenon_H1bc zenon_H1bd. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H1bf. zenon_intro zenon_H1be. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H1c1. zenon_intro zenon_H1c0. % 51.19/51.40 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H1c3. zenon_intro zenon_H1c2. % 51.19/51.40 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.40 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1bd. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H196. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e23)) = ((op2 (e23) (e23)) = (op2 (e21) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1c4. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1c2. % 51.19/51.41 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 51.19/51.41 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c6]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1c6. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H196. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (op2 (e21) (e23)) (op2 (e21) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 51.19/51.41 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1c5. apply sym_equal. exact zenon_H1bc. % 51.19/51.41 apply zenon_H1c5. apply sym_equal. exact zenon_H1bc. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H1c5. apply sym_equal. exact zenon_H1bc. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L134_ *) % 51.19/51.41 assert (zenon_L135_ : (~((op2 (e20) (e20)) = (op2 (op2 (e22) (e23)) (op2 (e22) (e23))))) -> ((op2 (e22) (e23)) = (e20)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1c8 zenon_H1c9. % 51.19/51.41 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 51.19/51.41 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1ca. apply sym_equal. exact zenon_H1c9. % 51.19/51.41 apply zenon_H1ca. apply sym_equal. exact zenon_H1c9. % 51.19/51.41 (* end of lemma zenon_L135_ *) % 51.19/51.41 assert (zenon_L136_ : (((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e20))/\(((op2 (op2 (e22) (e21)) (op2 (e22) (e21))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1cb zenon_H1cc zenon_H1c9 zenon_H1cd. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H1cf. zenon_intro zenon_H1ce. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d1. zenon_intro zenon_H1d0. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_H1d3. zenon_intro zenon_H1d2. % 51.19/51.41 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e23)) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1cc. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1d2. % 51.19/51.41 cut (((e23) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 51.19/51.41 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e20) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1d5. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H161. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (op2 (e22) (e23)) (op2 (e22) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L135_); trivial. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H1d4. apply sym_equal. exact zenon_H1cd. % 51.19/51.41 (* end of lemma zenon_L136_ *) % 51.19/51.41 assert (zenon_L137_ : (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e20))/\(((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e21))/\(((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1d6 zenon_H1d7 zenon_H1d8. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H1da. zenon_intro zenon_H1d9. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H1dc. zenon_intro zenon_H1db. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H1de. zenon_intro zenon_H1dd. % 51.19/51.41 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e22)) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1d7. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1de. % 51.19/51.41 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 51.19/51.41 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1e0]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e22) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1e0. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1a0. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (op2 (e23) (e22)) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 51.19/51.41 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1df. apply sym_equal. exact zenon_H1d8. % 51.19/51.41 apply zenon_H1df. apply sym_equal. exact zenon_H1d8. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H1df. apply sym_equal. exact zenon_H1d8. % 51.19/51.41 (* end of lemma zenon_L137_ *) % 51.19/51.41 assert (zenon_L138_ : ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H176 zenon_H156 zenon_H1b1 zenon_H1bd zenon_H1bc zenon_H1cd zenon_H1c9 zenon_H1cc zenon_H1d7 zenon_H1d8. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L133_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L134_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L136_); trivial. % 51.19/51.41 apply (zenon_L137_); trivial. % 51.19/51.41 (* end of lemma zenon_L138_ *) % 51.19/51.41 assert (zenon_L139_ : (~((op2 (e22) (e22)) = (op2 (op2 (e20) (e23)) (op2 (e20) (e23))))) -> ((op2 (e20) (e23)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1e4 zenon_H175. % 51.19/51.41 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 51.19/51.41 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1e5. apply sym_equal. exact zenon_H175. % 51.19/51.41 apply zenon_H1e5. apply sym_equal. exact zenon_H175. % 51.19/51.41 (* end of lemma zenon_L139_ *) % 51.19/51.41 assert (zenon_L140_ : (((op2 (op2 (e20) (e20)) (op2 (e20) (e20))) = (e20))/\(((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e21))/\(((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e22))/\((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1b0 zenon_H1e6 zenon_H175 zenon_H1e7. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_H1b3. zenon_intro zenon_H1b2. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b5. zenon_intro zenon_H1b4. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H1b7. zenon_intro zenon_H1b6. % 51.19/51.41 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e22) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1e6. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1b6. % 51.19/51.41 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 51.19/51.41 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1e9. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1a0. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (op2 (e20) (e23)) (op2 (e20) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L139_); trivial. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H1e8. apply sym_equal. exact zenon_H1e7. % 51.19/51.41 (* end of lemma zenon_L140_ *) % 51.19/51.41 assert (zenon_L141_ : (~((op2 (e20) (e20)) = (op2 (op2 (e21) (e23)) (op2 (e21) (e23))))) -> ((op2 (e21) (e23)) = (e20)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1ea zenon_H1a8. % 51.19/51.41 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 51.19/51.41 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1a9. apply sym_equal. exact zenon_H1a8. % 51.19/51.41 apply zenon_H1a9. apply sym_equal. exact zenon_H1a8. % 51.19/51.41 (* end of lemma zenon_L141_ *) % 51.19/51.41 assert (zenon_L142_ : (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e20))/\(((op2 (op2 (e21) (e21)) (op2 (e21) (e21))) = (e21))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e22))/\((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1bb zenon_H1cc zenon_H1a8 zenon_H1cd. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H1bf. zenon_intro zenon_H1be. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H1c1. zenon_intro zenon_H1c0. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H1c3. zenon_intro zenon_H1c2. % 51.19/51.41 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e23)) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1cc. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1c2. % 51.19/51.41 cut (((e23) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 51.19/51.41 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e20) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1eb. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H161. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (op2 (e21) (e23)) (op2 (e21) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1ea]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L141_); trivial. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H1d4. apply sym_equal. exact zenon_H1cd. % 51.19/51.41 (* end of lemma zenon_L142_ *) % 51.19/51.41 assert (zenon_L143_ : (((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e20))/\(((op2 (op2 (e22) (e21)) (op2 (e22) (e21))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e23))))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1cb zenon_H1e7 zenon_H1ec. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H1cf. zenon_intro zenon_H1ce. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d1. zenon_intro zenon_H1d0. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_H1d3. zenon_intro zenon_H1d2. % 51.19/51.41 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1ec. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H196. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e23)) = ((op2 (e23) (e23)) = (op2 (e22) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1ed. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1d2. % 51.19/51.41 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 51.19/51.41 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1ee. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H196. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (op2 (e22) (e23)) (op2 (e22) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 51.19/51.41 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1e8. apply sym_equal. exact zenon_H1e7. % 51.19/51.41 apply zenon_H1e8. apply sym_equal. exact zenon_H1e7. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H1e8. apply sym_equal. exact zenon_H1e7. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L143_ *) % 51.19/51.41 assert (zenon_L144_ : ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H175 zenon_H1e6 zenon_H1cd zenon_H1a8 zenon_H1cc zenon_H1ec zenon_H1e7 zenon_H1d7 zenon_H1d8. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L140_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L142_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L143_); trivial. % 51.19/51.41 apply (zenon_L137_); trivial. % 51.19/51.41 (* end of lemma zenon_L144_ *) % 51.19/51.41 assert (zenon_L145_ : (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e21)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1bd zenon_H14e zenon_H1f0. % 51.19/51.41 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1bd. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14e. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 51.19/51.41 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e21) = (op2 (e21) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1f1. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H188. % 51.19/51.41 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 51.19/51.41 cut (((op2 (e21) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H1f2 zenon_H1f0). % 51.19/51.41 apply zenon_H189. apply refl_equal. % 51.19/51.41 apply zenon_H189. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L145_ *) % 51.19/51.41 assert (zenon_L146_ : ((op2 (e22) (e23)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1e7 zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1bc zenon_H1cd zenon_H1c9 zenon_H1cc zenon_H1d7 zenon_H1d8. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L140_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L134_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L136_); trivial. % 51.19/51.41 apply (zenon_L137_); trivial. % 51.19/51.41 (* end of lemma zenon_L146_ *) % 51.19/51.41 assert (zenon_L147_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1f3 zenon_H1ec zenon_H14e zenon_H187 zenon_H14 zenon_H15e zenon_H1e7 zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cd zenon_H1c9 zenon_H1cc zenon_H1d7 zenon_H1d8. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1f4 ]. % 51.19/51.41 apply (zenon_L144_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f5 ]. % 51.19/51.41 apply (zenon_L145_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H186 | zenon_intro zenon_H1bc ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_L146_); trivial. % 51.19/51.41 (* end of lemma zenon_L147_ *) % 51.19/51.41 assert (zenon_L148_ : (~((e21) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1f6. % 51.19/51.41 apply zenon_H1f6. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L148_ *) % 51.19/51.41 assert (zenon_L149_ : (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e23)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1f7 zenon_H14e zenon_H1f8. % 51.19/51.41 cut (((e21) = (op2 (e23) (e23))) = ((e21) = (e23))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1f7. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14e. % 51.19/51.41 cut (((op2 (e23) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 51.19/51.41 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1f6. apply refl_equal. % 51.19/51.41 exact (zenon_H1f9 zenon_H1f8). % 51.19/51.41 (* end of lemma zenon_L149_ *) % 51.19/51.41 assert (zenon_L150_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H1b1 zenon_H156 zenon_H176 zenon_H1d8 zenon_H1d7 zenon_H1cc zenon_H1c9 zenon_H1cd zenon_H1bd zenon_H1e6 zenon_H175 zenon_H15e zenon_H14 zenon_H187 zenon_H1ec zenon_H1f3 zenon_H1f7 zenon_H14e. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.41 apply (zenon_L132_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.41 apply (zenon_L138_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_L147_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 (* end of lemma zenon_L150_ *) % 51.19/51.41 assert (zenon_L151_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1fd zenon_H14 zenon_H1fe zenon_H14e. % 51.19/51.41 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1fd. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14. % 51.19/51.41 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 51.19/51.41 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H201 ]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e20) = (op2 (e23) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1ff. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H200. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H202]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H202 zenon_H1fe). % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply (zenon_L112_); trivial. % 51.19/51.41 (* end of lemma zenon_L151_ *) % 51.19/51.41 assert (zenon_L152_ : ((op2 (e23) (e21)) = (e20)) -> ((op2 (e23) (e21)) = (e23)) -> (~((e20) = (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H203 zenon_H204 zenon_H205. % 51.19/51.41 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.41 cut (((e23) = (e23)) = ((e20) = (e23))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H205. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1ad. % 51.19/51.41 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.41 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (e23) (e21)) = (e20)) = ((e23) = (e20))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H206. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H203. % 51.19/51.41 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.41 cut (((op2 (e23) (e21)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H207 zenon_H204). % 51.19/51.41 apply zenon_H16c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L152_ *) % 51.19/51.41 assert (zenon_L153_ : ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H14 zenon_H208 zenon_H14e zenon_H209. % 51.19/51.41 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H20a | zenon_intro zenon_H20b ]. % 51.19/51.41 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((op2 (e23) (e21)) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H209. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H20a. % 51.19/51.41 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 51.19/51.41 cut (((op2 (e23) (e22)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e22)) = (op2 (e23) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H20c. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14. % 51.19/51.41 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 51.19/51.41 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H20a | zenon_intro zenon_H20b ]. % 51.19/51.41 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e20) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H20d. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H20a. % 51.19/51.41 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 51.19/51.41 cut (((op2 (e23) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H20e zenon_H208). % 51.19/51.41 apply zenon_H20b. apply refl_equal. % 51.19/51.41 apply zenon_H20b. apply refl_equal. % 51.19/51.41 apply (zenon_L112_); trivial. % 51.19/51.41 apply zenon_H20b. apply refl_equal. % 51.19/51.41 apply zenon_H20b. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L153_ *) % 51.19/51.41 assert (zenon_L154_ : ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e23)) = (e20)) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H14e zenon_H20f zenon_H210. % 51.19/51.41 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H211 | zenon_intro zenon_H1f6 ]. % 51.19/51.41 cut (((e21) = (e21)) = ((e20) = (e21))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H210. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H211. % 51.19/51.41 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.41 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e21) = (op2 (e23) (e23))) = ((e21) = (e20))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H212. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14e. % 51.19/51.41 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 51.19/51.41 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1f6. apply refl_equal. % 51.19/51.41 exact (zenon_H213 zenon_H20f). % 51.19/51.41 apply zenon_H1f6. apply refl_equal. % 51.19/51.41 apply zenon_H1f6. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L154_ *) % 51.19/51.41 assert (zenon_L155_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e23))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H205 zenon_H204 zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.41 apply (zenon_L151_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.41 apply (zenon_L152_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.41 apply (zenon_L153_); trivial. % 51.19/51.41 apply (zenon_L154_); trivial. % 51.19/51.41 (* end of lemma zenon_L155_ *) % 51.19/51.41 assert (zenon_L156_ : (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e20)) = (e21)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H217 zenon_H14e zenon_H218. % 51.19/51.41 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e20)) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H217. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14e. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H201 ]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e21) = (op2 (e23) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H219. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H200. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H21a zenon_H218). % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L156_ *) % 51.19/51.41 assert (zenon_L157_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H21b zenon_H21c zenon_H1d8. % 51.19/51.41 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H21b. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H21c. % 51.19/51.41 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply zenon_H1df. apply sym_equal. exact zenon_H1d8. % 51.19/51.41 (* end of lemma zenon_L157_ *) % 51.19/51.41 assert (zenon_L158_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H21b zenon_H1cd zenon_H21d. % 51.19/51.41 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H21b. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1cd. % 51.19/51.41 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply zenon_H21e. apply sym_equal. exact zenon_H21d. % 51.19/51.41 (* end of lemma zenon_L158_ *) % 51.19/51.41 assert (zenon_L159_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H21f zenon_H14 zenon_H1fd zenon_H14e zenon_H217 zenon_H1d8 zenon_H21b zenon_H21d. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H220 ]. % 51.19/51.41 apply (zenon_L151_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H218 | zenon_intro zenon_H221 ]. % 51.19/51.41 apply (zenon_L156_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H21c | zenon_intro zenon_H1cd ]. % 51.19/51.41 apply (zenon_L157_); trivial. % 51.19/51.41 apply (zenon_L158_); trivial. % 51.19/51.41 (* end of lemma zenon_L159_ *) % 51.19/51.41 assert (zenon_L160_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H222 zenon_H1f3 zenon_H1ec zenon_H187 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1c9 zenon_H1cc zenon_H1d7 zenon_H176 zenon_H156 zenon_H1b1 zenon_H1ac zenon_H1fa zenon_H210 zenon_H209 zenon_H205 zenon_H214 zenon_H21b zenon_H1d8 zenon_H217 zenon_H1fd zenon_H14 zenon_H21f zenon_H1f7 zenon_H14e. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.19/51.41 apply (zenon_L150_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.19/51.41 apply (zenon_L155_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_L159_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 (* end of lemma zenon_L160_ *) % 51.19/51.41 assert (zenon_L161_ : (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e22) (e21)) = (e22)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H225 zenon_H176 zenon_H226. % 51.19/51.41 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (e22) (e20)) = (op2 (e22) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H225. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H176. % 51.19/51.41 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 51.19/51.41 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H228. apply refl_equal. % 51.19/51.41 apply zenon_H227. apply sym_equal. exact zenon_H226. % 51.19/51.41 (* end of lemma zenon_L161_ *) % 51.19/51.41 assert (zenon_L162_ : ((op2 (e23) (e21)) = (e20)) -> ((op2 (e23) (e21)) = (e22)) -> (~((e20) = (e22))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H203 zenon_H229 zenon_H16f. % 51.19/51.41 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H170 | zenon_intro zenon_H171 ]. % 51.19/51.41 cut (((e22) = (e22)) = ((e20) = (e22))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H16f. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H170. % 51.19/51.41 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.19/51.41 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (e23) (e21)) = (e20)) = ((e22) = (e20))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H172. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H203. % 51.19/51.41 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.41 cut (((op2 (e23) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H22a zenon_H229). % 51.19/51.41 apply zenon_H16c. apply refl_equal. % 51.19/51.41 apply zenon_H171. apply refl_equal. % 51.19/51.41 apply zenon_H171. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L162_ *) % 51.19/51.41 assert (zenon_L163_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> ((op2 (e23) (e21)) = (e22)) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H16f zenon_H229 zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.41 apply (zenon_L151_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.41 apply (zenon_L162_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.41 apply (zenon_L153_); trivial. % 51.19/51.41 apply (zenon_L154_); trivial. % 51.19/51.41 (* end of lemma zenon_L163_ *) % 51.19/51.41 assert (zenon_L164_ : (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H22b zenon_H164 zenon_H195 zenon_H15e zenon_H18e zenon_H187 zenon_H17f zenon_H180 zenon_H19b zenon_H176 zenon_H225 zenon_H214 zenon_H1fd zenon_H16f zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H165 | zenon_intro zenon_H22c ]. % 51.19/51.41 apply (zenon_L117_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H17c | zenon_intro zenon_H22d ]. % 51.19/51.41 apply (zenon_L127_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H226 | zenon_intro zenon_H229 ]. % 51.19/51.41 apply (zenon_L161_); trivial. % 51.19/51.41 apply (zenon_L163_); trivial. % 51.19/51.41 (* end of lemma zenon_L164_ *) % 51.19/51.41 assert (zenon_L165_ : (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e20)) = (e22)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H22e zenon_H222 zenon_H1f3 zenon_H1ec zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H156 zenon_H1b1 zenon_H1ac zenon_H1fa zenon_H205 zenon_H21b zenon_H217 zenon_H21f zenon_H1f7 zenon_H1a7 zenon_H16d zenon_H22f zenon_H19f zenon_H168 zenon_H230 zenon_H210 zenon_H14e zenon_H209 zenon_H16f zenon_H1fd zenon_H214 zenon_H225 zenon_H176 zenon_H19b zenon_H180 zenon_H18e zenon_H195 zenon_H164 zenon_H22b zenon_H15e zenon_H14 zenon_H187. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H16e | zenon_intro zenon_H231 ]. % 51.19/51.41 apply (zenon_L120_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17c | zenon_intro zenon_H232 ]. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H169 | zenon_intro zenon_H233 ]. % 51.19/51.41 apply (zenon_L118_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H17f | zenon_intro zenon_H234 ]. % 51.19/51.41 apply (zenon_L127_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H19e | zenon_intro zenon_H1d8 ]. % 51.19/51.41 apply (zenon_L128_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.41 apply (zenon_L129_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.41 apply (zenon_L130_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.41 apply (zenon_L160_); trivial. % 51.19/51.41 apply (zenon_L154_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17f | zenon_intro zenon_H186 ]. % 51.19/51.41 apply (zenon_L164_); trivial. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 (* end of lemma zenon_L165_ *) % 51.19/51.41 assert (zenon_L166_ : ((op2 (e20) (e20)) = (e21)) -> ((op2 (e20) (e20)) = (e23)) -> (~((e21) = (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H237 zenon_H238 zenon_H1f7. % 51.19/51.41 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.41 cut (((e23) = (e23)) = ((e21) = (e23))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1f7. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1ad. % 51.19/51.41 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.41 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (e20) (e20)) = (e21)) = ((e23) = (e21))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H239. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H237. % 51.19/51.41 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H23a zenon_H238). % 51.19/51.41 apply zenon_H1f6. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L166_ *) % 51.19/51.41 assert (zenon_L167_ : (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1a7 zenon_H23b zenon_H1bc. % 51.19/51.41 cut (((op2 (e21) (e20)) = (e23)) = ((op2 (e21) (e20)) = (op2 (e21) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1a7. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H23b. % 51.19/51.41 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 51.19/51.41 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1aa. apply refl_equal. % 51.19/51.41 apply zenon_H1c5. apply sym_equal. exact zenon_H1bc. % 51.19/51.41 (* end of lemma zenon_L167_ *) % 51.19/51.41 assert (zenon_L168_ : (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e22)) = (e21)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H23c zenon_H14e zenon_H23d. % 51.19/51.41 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e22)) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H23c. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14e. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H20a | zenon_intro zenon_H20b ]. % 51.19/51.41 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e21) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H23e. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H20a. % 51.19/51.41 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H20b]. % 51.19/51.41 cut (((op2 (e23) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H23f]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H23f zenon_H23d). % 51.19/51.41 apply zenon_H20b. apply refl_equal. % 51.19/51.41 apply zenon_H20b. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L168_ *) % 51.19/51.41 assert (zenon_L169_ : (((op2 (op2 (e20) (e20)) (op2 (e20) (e20))) = (e20))/\(((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e21))/\(((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e22))/\((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1b0 zenon_H1d7 zenon_H175 zenon_H21d. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_H1b3. zenon_intro zenon_H1b2. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b5. zenon_intro zenon_H1b4. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H1b7. zenon_intro zenon_H1b6. % 51.19/51.41 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1d7. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1b6. % 51.19/51.41 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 51.19/51.41 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1e9. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1a0. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (op2 (e20) (e23)) (op2 (e20) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L139_); trivial. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H21e. apply sym_equal. exact zenon_H21d. % 51.19/51.41 (* end of lemma zenon_L169_ *) % 51.19/51.41 assert (zenon_L170_ : (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e20))/\(((op2 (op2 (e21) (e21)) (op2 (e21) (e21))) = (e21))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e22))/\((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1bb zenon_H240 zenon_H1a8 zenon_H23b. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H1bf. zenon_intro zenon_H1be. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H1c1. zenon_intro zenon_H1c0. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H1c3. zenon_intro zenon_H1c2. % 51.19/51.41 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e23)) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H240. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1c2. % 51.19/51.41 cut (((e23) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 51.19/51.41 cut (((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (op2 (e20) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1eb. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H161. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (op2 (e21) (e23)) (op2 (e21) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1ea]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L141_); trivial. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H241. apply sym_equal. exact zenon_H23b. % 51.19/51.41 (* end of lemma zenon_L170_ *) % 51.19/51.41 assert (zenon_L171_ : (~((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H242 zenon_H14e. % 51.19/51.41 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 51.19/51.41 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H243 zenon_H14e). % 51.19/51.41 exact (zenon_H243 zenon_H14e). % 51.19/51.41 (* end of lemma zenon_L171_ *) % 51.19/51.41 assert (zenon_L172_ : (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e20))/\(((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e21))/\(((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1d6 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H1da. zenon_intro zenon_H1d9. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H1dc. zenon_intro zenon_H1db. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H1de. zenon_intro zenon_H1dd. % 51.19/51.41 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H246 | zenon_intro zenon_H247 ]. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (e20) (e21)) = (op2 (e21) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H245. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H246. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H248]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23)) = ((op2 (e21) (e21)) = (op2 (e20) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H248. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1dd. % 51.19/51.41 cut (((e23) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H249]. % 51.19/51.41 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H246 | zenon_intro zenon_H247 ]. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H24a. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H246. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L171_); trivial. % 51.19/51.41 apply zenon_H247. apply refl_equal. % 51.19/51.41 apply zenon_H247. apply refl_equal. % 51.19/51.41 apply zenon_H249. apply sym_equal. exact zenon_H244. % 51.19/51.41 apply zenon_H247. apply refl_equal. % 51.19/51.41 apply zenon_H247. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L172_ *) % 51.19/51.41 assert (zenon_L173_ : ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H21d zenon_H175 zenon_H1d7 zenon_H23b zenon_H1a8 zenon_H240 zenon_H1ec zenon_H1e7 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L169_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L170_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L143_); trivial. % 51.19/51.41 apply (zenon_L172_); trivial. % 51.19/51.41 (* end of lemma zenon_L173_ *) % 51.19/51.41 assert (zenon_L174_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H24b zenon_H209 zenon_H14 zenon_H23c zenon_H21c zenon_H21b zenon_H175 zenon_H1d7 zenon_H23b zenon_H1a8 zenon_H240 zenon_H1ec zenon_H1e7 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H208 | zenon_intro zenon_H24c ]. % 51.19/51.41 apply (zenon_L153_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H23d | zenon_intro zenon_H24d ]. % 51.19/51.41 apply (zenon_L168_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H21d ]. % 51.19/51.41 apply (zenon_L157_); trivial. % 51.19/51.41 apply (zenon_L173_); trivial. % 51.19/51.41 (* end of lemma zenon_L174_ *) % 51.19/51.41 assert (zenon_L175_ : ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1bc zenon_H1ec zenon_H1e7 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L140_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L134_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L143_); trivial. % 51.19/51.41 apply (zenon_L172_); trivial. % 51.19/51.41 (* end of lemma zenon_L175_ *) % 51.19/51.41 assert (zenon_L176_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1f3 zenon_H240 zenon_H23b zenon_H1d7 zenon_H21b zenon_H21c zenon_H23c zenon_H209 zenon_H24b zenon_H187 zenon_H14 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1ec zenon_H1e7 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1f4 ]. % 51.19/51.41 apply (zenon_L174_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f5 ]. % 51.19/51.41 apply (zenon_L145_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H186 | zenon_intro zenon_H1bc ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_L175_); trivial. % 51.19/51.41 (* end of lemma zenon_L176_ *) % 51.19/51.41 assert (zenon_L177_ : ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H175 zenon_H1e6 zenon_H1cd zenon_H1a8 zenon_H1cc zenon_H1ec zenon_H1e7 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L140_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L142_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L143_); trivial. % 51.19/51.41 apply (zenon_L172_); trivial. % 51.19/51.41 (* end of lemma zenon_L177_ *) % 51.19/51.41 assert (zenon_L178_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H19b zenon_H245 zenon_H244 zenon_H14e zenon_H1e7 zenon_H1ec zenon_H1cc zenon_H1a8 zenon_H1cd zenon_H1e6 zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.19/51.41 apply (zenon_L177_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.19/51.41 apply (zenon_L125_); trivial. % 51.19/51.41 apply (zenon_L126_); trivial. % 51.19/51.41 (* end of lemma zenon_L178_ *) % 51.19/51.41 assert (zenon_L179_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1f3 zenon_H195 zenon_H18e zenon_H1cd zenon_H1cc zenon_H19b zenon_H187 zenon_H14 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1ec zenon_H1e7 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1f4 ]. % 51.19/51.41 apply (zenon_L178_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f5 ]. % 51.19/51.41 apply (zenon_L145_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H186 | zenon_intro zenon_H1bc ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_L175_); trivial. % 51.19/51.41 (* end of lemma zenon_L179_ *) % 51.19/51.41 assert (zenon_L180_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H21f zenon_H1fd zenon_H217 zenon_H1d8 zenon_H21b zenon_H1f3 zenon_H195 zenon_H18e zenon_H1cc zenon_H19b zenon_H187 zenon_H14 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1ec zenon_H1e7 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H220 ]. % 51.19/51.41 apply (zenon_L151_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H218 | zenon_intro zenon_H221 ]. % 51.19/51.41 apply (zenon_L156_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H21c | zenon_intro zenon_H1cd ]. % 51.19/51.41 apply (zenon_L157_); trivial. % 51.19/51.41 apply (zenon_L179_); trivial. % 51.19/51.41 (* end of lemma zenon_L180_ *) % 51.19/51.41 assert (zenon_L181_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((e20) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H24e zenon_H24b zenon_H23c zenon_H1d7 zenon_H23b zenon_H240 zenon_H210 zenon_H209 zenon_H16f zenon_H214 zenon_H245 zenon_H244 zenon_H14e zenon_H1e7 zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H175 zenon_H187 zenon_H19b zenon_H1cc zenon_H18e zenon_H1f3 zenon_H21b zenon_H217 zenon_H1fd zenon_H21f zenon_H15e zenon_H14 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.19/51.41 apply (zenon_L176_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.19/51.41 apply (zenon_L163_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.19/51.41 apply (zenon_L180_); trivial. % 51.19/51.41 apply (zenon_L126_); trivial. % 51.19/51.41 (* end of lemma zenon_L181_ *) % 51.19/51.41 assert (zenon_L182_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e21))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((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))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H1a7 zenon_H195 zenon_H14 zenon_H15e zenon_H21f zenon_H1fd zenon_H217 zenon_H21b zenon_H1f3 zenon_H18e zenon_H1cc zenon_H19b zenon_H187 zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1ec zenon_H244 zenon_H245 zenon_H214 zenon_H16f zenon_H209 zenon_H210 zenon_H240 zenon_H23b zenon_H1d7 zenon_H23c zenon_H24b zenon_H24e zenon_H1f7 zenon_H14e. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.41 apply (zenon_L132_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.41 apply (zenon_L167_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_L181_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 (* end of lemma zenon_L182_ *) % 51.19/51.41 assert (zenon_L183_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H19b zenon_H16f zenon_H1a5 zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.19/51.41 apply (zenon_L129_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.19/51.41 apply (zenon_L125_); trivial. % 51.19/51.41 apply (zenon_L126_); trivial. % 51.19/51.41 (* end of lemma zenon_L183_ *) % 51.19/51.41 assert (zenon_L184_ : ((op2 (e21) (e23)) = (e20)) -> ((op2 (e21) (e23)) = (e23)) -> (~((e20) = (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1a8 zenon_H1bc zenon_H205. % 51.19/51.41 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.41 cut (((e23) = (e23)) = ((e20) = (e23))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H205. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1ad. % 51.19/51.41 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.41 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (e21) (e23)) = (e20)) = ((e23) = (e20))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H206. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1a8. % 51.19/51.41 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.41 cut (((op2 (e21) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H251]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H251 zenon_H1bc). % 51.19/51.41 apply zenon_H16c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L184_ *) % 51.19/51.41 assert (zenon_L185_ : (((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e20))/\(((op2 (op2 (e22) (e21)) (op2 (e22) (e21))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e22) (e20)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1cb zenon_H1b1 zenon_H1c9 zenon_H252. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H1cf. zenon_intro zenon_H1ce. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d1. zenon_intro zenon_H1d0. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d0). zenon_intro zenon_H1d3. zenon_intro zenon_H1d2. % 51.19/51.41 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e23)) = ((op2 (e20) (e20)) = (op2 (e22) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1b1. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1d2. % 51.19/51.41 cut (((e23) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 51.19/51.41 cut (((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H161 | zenon_intro zenon_H162 ]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (op2 (e20) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1d5. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H161. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H162]. % 51.19/51.41 cut (((op2 (e20) (e20)) = (op2 (op2 (e22) (e23)) (op2 (e22) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L135_); trivial. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H162. apply refl_equal. % 51.19/51.41 apply zenon_H253. apply sym_equal. exact zenon_H252. % 51.19/51.41 (* end of lemma zenon_L185_ *) % 51.19/51.41 assert (zenon_L186_ : ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H21d zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H252 zenon_H1c9 zenon_H1b1 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L169_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L134_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L185_); trivial. % 51.19/51.41 apply (zenon_L172_); trivial. % 51.19/51.41 (* end of lemma zenon_L186_ *) % 51.19/51.41 assert (zenon_L187_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H24b zenon_H209 zenon_H14 zenon_H23c zenon_H21c zenon_H21b zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H252 zenon_H1c9 zenon_H1b1 zenon_H14e zenon_H244 zenon_H245. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H208 | zenon_intro zenon_H24c ]. % 51.19/51.41 apply (zenon_L153_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H23d | zenon_intro zenon_H24d ]. % 51.19/51.41 apply (zenon_L168_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H21d ]. % 51.19/51.41 apply (zenon_L157_); trivial. % 51.19/51.41 apply (zenon_L186_); trivial. % 51.19/51.41 (* end of lemma zenon_L187_ *) % 51.19/51.41 assert (zenon_L188_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H22f zenon_H195 zenon_H15e zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H205 zenon_H245 zenon_H244 zenon_H1b1 zenon_H252 zenon_H1bc zenon_H1bd zenon_H1d7 zenon_H175 zenon_H21b zenon_H21c zenon_H23c zenon_H14 zenon_H209 zenon_H24b zenon_H14e zenon_H210. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.41 apply (zenon_L183_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.41 apply (zenon_L184_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.41 apply (zenon_L187_); trivial. % 51.19/51.41 apply (zenon_L154_); trivial. % 51.19/51.41 (* end of lemma zenon_L188_ *) % 51.19/51.41 assert (zenon_L189_ : (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H254 zenon_H252 zenon_H1e7. % 51.19/51.41 cut (((op2 (e22) (e20)) = (e23)) = ((op2 (e22) (e20)) = (op2 (e22) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H254. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H252. % 51.19/51.41 cut (((e23) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 51.19/51.41 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H228. apply refl_equal. % 51.19/51.41 apply zenon_H1e8. apply sym_equal. exact zenon_H1e7. % 51.19/51.41 (* end of lemma zenon_L189_ *) % 51.19/51.41 assert (zenon_L190_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H210 zenon_H24b zenon_H209 zenon_H14 zenon_H23c zenon_H21c zenon_H21b zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H244 zenon_H245 zenon_H205 zenon_H19b zenon_H16f zenon_H187 zenon_H18e zenon_H15e zenon_H195 zenon_H22f zenon_H252 zenon_H254 zenon_H1f7 zenon_H14e. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.41 apply (zenon_L132_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.41 apply (zenon_L188_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_L189_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 (* end of lemma zenon_L190_ *) % 51.19/51.41 assert (zenon_L191_ : ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e23)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H14e zenon_H1f7 zenon_H254 zenon_H252 zenon_H22f zenon_H16f zenon_H19b zenon_H205 zenon_H245 zenon_H244 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H21b zenon_H21c zenon_H23c zenon_H209 zenon_H24b zenon_H210 zenon_H1ac zenon_H1fa zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.19/51.41 apply (zenon_L190_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.19/51.41 apply (zenon_L125_); trivial. % 51.19/51.41 apply (zenon_L126_); trivial. % 51.19/51.41 (* end of lemma zenon_L191_ *) % 51.19/51.41 assert (zenon_L192_ : ((op2 (e23) (e20)) = (e22)) -> ((op2 (e23) (e20)) = (e23)) -> (~((e22) = (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H21c zenon_H1cd zenon_H1ac. % 51.19/51.41 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.41 cut (((e23) = (e23)) = ((e22) = (e23))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1ac. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1ad. % 51.19/51.41 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.41 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (e23) (e20)) = (e22)) = ((e23) = (e22))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1ae. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H21c. % 51.19/51.41 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H255]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H255 zenon_H1cd). % 51.19/51.41 apply zenon_H171. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L192_ *) % 51.19/51.41 assert (zenon_L193_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e22)) = (e23)) -> (~((e20) = (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H156 zenon_H256 zenon_H205. % 51.19/51.41 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.41 cut (((e23) = (e23)) = ((e20) = (e23))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H205. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1ad. % 51.19/51.41 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.41 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (e20) (e22)) = (e20)) = ((e23) = (e20))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H206. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H156. % 51.19/51.41 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.41 cut (((op2 (e20) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H257 zenon_H256). % 51.19/51.41 apply zenon_H16c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 apply zenon_H14c. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L193_ *) % 51.19/51.41 assert (zenon_L194_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H19b zenon_H1ac zenon_H1ab zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.19/51.41 apply (zenon_L132_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.19/51.41 apply (zenon_L125_); trivial. % 51.19/51.41 apply (zenon_L126_); trivial. % 51.19/51.41 (* end of lemma zenon_L194_ *) % 51.19/51.41 assert (zenon_L195_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e20)) = (e21)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e20) = (e23))) -> ((op2 (e20) (e22)) = (e20)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H258 zenon_H21c zenon_H14e zenon_H1f7 zenon_H254 zenon_H22f zenon_H16f zenon_H245 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H21b zenon_H23c zenon_H209 zenon_H24b zenon_H210 zenon_H1fa zenon_H1a7 zenon_H21f zenon_H1fd zenon_H217 zenon_H1f3 zenon_H1cc zenon_H175 zenon_H1e6 zenon_H1ec zenon_H214 zenon_H240 zenon_H24e zenon_H237 zenon_H259 zenon_H205 zenon_H156 zenon_H19b zenon_H1ac zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.19/51.41 apply (zenon_L166_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.19/51.41 apply (zenon_L166_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.19/51.41 apply (zenon_L182_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.19/51.41 apply (zenon_L191_); trivial. % 51.19/51.41 apply (zenon_L192_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.19/51.41 apply (zenon_L193_); trivial. % 51.19/51.41 apply (zenon_L194_); trivial. % 51.19/51.41 (* end of lemma zenon_L195_ *) % 51.19/51.41 assert (zenon_L196_ : ((op2 (e20) (e21)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H25e zenon_H237 zenon_H25f. % 51.19/51.41 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H153 | zenon_intro zenon_H154 ]. % 51.19/51.41 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((op2 (e20) (e20)) = (op2 (e20) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H25f. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H153. % 51.19/51.41 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 51.19/51.41 cut (((op2 (e20) (e21)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H260]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (e20) (e21)) = (e21)) = ((op2 (e20) (e21)) = (op2 (e20) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H260. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H25e. % 51.19/51.41 cut (((e21) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 51.19/51.41 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H154. apply refl_equal. % 51.19/51.41 apply zenon_H261. apply sym_equal. exact zenon_H237. % 51.19/51.41 apply zenon_H154. apply refl_equal. % 51.19/51.41 apply zenon_H154. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L196_ *) % 51.19/51.41 assert (zenon_L197_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e20)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H15e zenon_H21c zenon_H175 zenon_H176 zenon_H14 zenon_H262. % 51.19/51.41 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H201 ]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e22) (e20)) = (op2 (e23) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H262. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H200. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((op2 (e23) (e20)) = (op2 (e22) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H263. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H15e. % 51.19/51.41 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H174]. % 51.19/51.41 cut (((e22) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H200 | zenon_intro zenon_H201 ]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e22) = (op2 (e23) (e20)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H264. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H200. % 51.19/51.41 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 51.19/51.41 cut (((op2 (e23) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H265 zenon_H21c). % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply (zenon_L121_); trivial. % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 apply zenon_H201. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L197_ *) % 51.19/51.41 assert (zenon_L198_ : (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> ((op2 (e22) (e23)) = (e20)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H254 zenon_H266 zenon_H1c9. % 51.19/51.41 cut (((op2 (e22) (e20)) = (e20)) = ((op2 (e22) (e20)) = (op2 (e22) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H254. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H266. % 51.19/51.41 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 51.19/51.41 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H228. apply refl_equal. % 51.19/51.41 apply zenon_H1ca. apply sym_equal. exact zenon_H1c9. % 51.19/51.41 (* end of lemma zenon_L198_ *) % 51.19/51.41 assert (zenon_L199_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e23))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H22f zenon_H16f zenon_H175 zenon_H205 zenon_H1bc zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.41 apply (zenon_L129_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.41 apply (zenon_L184_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.41 apply (zenon_L198_); trivial. % 51.19/51.41 apply (zenon_L154_); trivial. % 51.19/51.41 (* end of lemma zenon_L199_ *) % 51.19/51.41 assert (zenon_L200_ : (((op2 (op2 (e21) (e20)) (op2 (e21) (e20))) = (e20))/\(((op2 (op2 (e21) (e21)) (op2 (e21) (e21))) = (e21))/\(((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e22))/\((op2 (op2 (e21) (e23)) (op2 (e21) (e23))) = (e23))))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1bb zenon_H17f zenon_H267. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1bb). zenon_intro zenon_H1bf. zenon_intro zenon_H1be. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1be). zenon_intro zenon_H1c1. zenon_intro zenon_H1c0. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1c0). zenon_intro zenon_H1c3. zenon_intro zenon_H1c2. % 51.19/51.41 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e21) (e22)) = (op2 (e22) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H267. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1a0. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (e22)) = ((op2 (e22) (e22)) = (op2 (e21) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H268. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1c3. % 51.19/51.41 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 51.19/51.41 cut (((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e21) (e22)) (op2 (e21) (e22))) = (op2 (e22) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H269. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1a0. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.41 cut (((op2 (e22) (e22)) = (op2 (op2 (e21) (e22)) (op2 (e21) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 51.19/51.41 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H184. apply sym_equal. exact zenon_H17f. % 51.19/51.41 apply zenon_H184. apply sym_equal. exact zenon_H17f. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H184. apply sym_equal. exact zenon_H17f. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 apply zenon_H1a1. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L200_ *) % 51.19/51.41 assert (zenon_L201_ : (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e20))/\(((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e21))/\(((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1d6 zenon_H21d zenon_H175 zenon_H195. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H1da. zenon_intro zenon_H1d9. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H1dc. zenon_intro zenon_H1db. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H1de. zenon_intro zenon_H1dd. % 51.19/51.41 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H195. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H196. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H198]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e22)) = ((op2 (e23) (e23)) = (op2 (e20) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H198. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1de. % 51.19/51.41 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 51.19/51.41 cut (((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (op2 (e23) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H26b. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H196. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.41 cut (((op2 (e23) (e23)) = (op2 (op2 (e23) (e22)) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 51.19/51.41 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H21e. apply sym_equal. exact zenon_H21d. % 51.19/51.41 apply zenon_H21e. apply sym_equal. exact zenon_H21d. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H1e5. apply sym_equal. exact zenon_H175. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 apply zenon_H197. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L201_ *) % 51.19/51.41 assert (zenon_L202_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1d7 zenon_H267 zenon_H17f zenon_H1ec zenon_H1e7 zenon_H21d zenon_H175 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L169_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L200_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L143_); trivial. % 51.19/51.41 apply (zenon_L201_); trivial. % 51.19/51.41 (* end of lemma zenon_L202_ *) % 51.19/51.41 assert (zenon_L203_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H210 zenon_H254 zenon_H266 zenon_H205 zenon_H16f zenon_H22f zenon_H195 zenon_H175 zenon_H21d zenon_H1ec zenon_H17f zenon_H267 zenon_H1d7 zenon_H1f7 zenon_H14e. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.41 apply (zenon_L132_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.41 apply (zenon_L199_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_L202_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 (* end of lemma zenon_L203_ *) % 51.19/51.41 assert (zenon_L204_ : (((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e20))/\(((op2 (op2 (e22) (e21)) (op2 (e22) (e21))) = (e21))/\(((op2 (op2 (e22) (e22)) (op2 (e22) (e22))) = (e22))/\((op2 (op2 (e22) (e23)) (op2 (e22) (e23))) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e23) (e21)) = (e20)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1cb zenon_H26d zenon_H26e zenon_H203. % 51.19/51.41 apply (zenon_and_s _ _ zenon_H1cb). zenon_intro zenon_H1cf. zenon_intro zenon_H1ce. % 51.19/51.41 cut (((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (e20)) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H26d. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H1cf. % 51.19/51.41 cut (((e20) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 51.19/51.41 cut (((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H246 | zenon_intro zenon_H247 ]. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e22) (e20)) (op2 (e22) (e20))) = (op2 (e21) (e21)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H270. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H246. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 51.19/51.41 cut (((op2 (e21) (e21)) = (op2 (op2 (e22) (e20)) (op2 (e22) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e21) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 51.19/51.41 cut (((e21) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H272. apply sym_equal. exact zenon_H26e. % 51.19/51.41 apply zenon_H272. apply sym_equal. exact zenon_H26e. % 51.19/51.41 apply zenon_H247. apply refl_equal. % 51.19/51.41 apply zenon_H247. apply refl_equal. % 51.19/51.41 apply zenon_H26f. apply sym_equal. exact zenon_H203. % 51.19/51.41 (* end of lemma zenon_L204_ *) % 51.19/51.41 assert (zenon_L205_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H203 zenon_H26e zenon_H26d zenon_H21d zenon_H175 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L169_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L134_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L204_); trivial. % 51.19/51.41 apply (zenon_L201_); trivial. % 51.19/51.41 (* end of lemma zenon_L205_ *) % 51.19/51.41 assert (zenon_L206_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1d7 zenon_H267 zenon_H17f zenon_H252 zenon_H1c9 zenon_H1b1 zenon_H21d zenon_H175 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L169_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L200_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L185_); trivial. % 51.19/51.41 apply (zenon_L201_); trivial. % 51.19/51.41 (* end of lemma zenon_L206_ *) % 51.19/51.41 assert (zenon_L207_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e21))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H273 zenon_H14e zenon_H1f7 zenon_H1ec zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H210 zenon_H1ac zenon_H1fa zenon_H26d zenon_H203 zenon_H1bc zenon_H1bd zenon_H226 zenon_H225 zenon_H1d7 zenon_H267 zenon_H17f zenon_H1c9 zenon_H1b1 zenon_H21d zenon_H175 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H266 | zenon_intro zenon_H274 ]. % 51.19/51.41 apply (zenon_L203_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H26e | zenon_intro zenon_H275 ]. % 51.19/51.41 apply (zenon_L205_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H176 | zenon_intro zenon_H252 ]. % 51.19/51.41 apply (zenon_L161_); trivial. % 51.19/51.41 apply (zenon_L206_); trivial. % 51.19/51.41 (* end of lemma zenon_L207_ *) % 51.19/51.41 assert (zenon_L208_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e21))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H222 zenon_H21c zenon_H14 zenon_H209 zenon_H1fd zenon_H214 zenon_H1d7 zenon_H267 zenon_H17f zenon_H1ec zenon_H175 zenon_H195 zenon_H273 zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H210 zenon_H1ac zenon_H1fa zenon_H26d zenon_H203 zenon_H1bd zenon_H226 zenon_H225 zenon_H1c9 zenon_H1b1 zenon_H1f7 zenon_H14e. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.19/51.41 apply (zenon_L192_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.19/51.41 apply (zenon_L155_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.41 apply (zenon_L132_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.41 apply (zenon_L207_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_L202_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 (* end of lemma zenon_L208_ *) % 51.19/51.41 assert (zenon_L209_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H15e zenon_H18e zenon_H187 zenon_H19b zenon_H16d zenon_H1a7 zenon_H1f7 zenon_H1b1 zenon_H225 zenon_H226 zenon_H1bd zenon_H203 zenon_H26d zenon_H1fa zenon_H1ac zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H273 zenon_H195 zenon_H175 zenon_H1ec zenon_H17f zenon_H267 zenon_H1d7 zenon_H214 zenon_H1fd zenon_H209 zenon_H14 zenon_H21c zenon_H222 zenon_H14e zenon_H210. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.41 apply (zenon_L183_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.41 apply (zenon_L130_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.41 apply (zenon_L208_); trivial. % 51.19/51.41 apply (zenon_L154_); trivial. % 51.19/51.41 (* end of lemma zenon_L209_ *) % 51.19/51.41 assert (zenon_L210_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H252 zenon_H1c9 zenon_H1b1 zenon_H21d zenon_H175 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.41 apply (zenon_L169_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.41 apply (zenon_L134_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.41 apply (zenon_L185_); trivial. % 51.19/51.41 apply (zenon_L201_); trivial. % 51.19/51.41 (* end of lemma zenon_L210_ *) % 51.19/51.41 assert (zenon_L211_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H273 zenon_H210 zenon_H14e zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H26d zenon_H203 zenon_H19f zenon_H14 zenon_H19e zenon_H15e zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H1c9 zenon_H1b1 zenon_H21d zenon_H175 zenon_H195. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H266 | zenon_intro zenon_H274 ]. % 51.19/51.41 apply (zenon_L199_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H26e | zenon_intro zenon_H275 ]. % 51.19/51.41 apply (zenon_L205_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H176 | zenon_intro zenon_H252 ]. % 51.19/51.41 apply (zenon_L128_); trivial. % 51.19/51.41 apply (zenon_L210_); trivial. % 51.19/51.41 (* end of lemma zenon_L211_ *) % 51.19/51.41 assert (zenon_L212_ : (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H18e zenon_H187 zenon_H19b zenon_H195 zenon_H175 zenon_H21d zenon_H1b1 zenon_H1bc zenon_H1bd zenon_H1d7 zenon_H15e zenon_H19e zenon_H14 zenon_H19f zenon_H203 zenon_H26d zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H273 zenon_H14e zenon_H210. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.41 apply (zenon_L183_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.41 apply (zenon_L184_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.41 apply (zenon_L211_); trivial. % 51.19/51.41 apply (zenon_L154_); trivial. % 51.19/51.41 (* end of lemma zenon_L212_ *) % 51.19/51.41 assert (zenon_L213_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e21) (e22)))) -> ((op2 (e23) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e22)) = (e20)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H276 zenon_H203 zenon_H14e zenon_H277. % 51.19/51.41 cut (((op2 (e23) (e21)) = (e20)) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (e21) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H276. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H203. % 51.19/51.41 cut (((e20) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 51.19/51.41 cut (((op2 (e23) (e21)) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [ zenon_intro zenon_H27a | zenon_intro zenon_H27b ]. % 51.19/51.41 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e21)) = (op2 (e23) (op2 (e23) (e23))))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H279. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H27a. % 51.19/51.41 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 51.19/51.41 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 51.19/51.41 congruence. % 51.19/51.41 apply (zenon_L112_); trivial. % 51.19/51.41 apply zenon_H27b. apply refl_equal. % 51.19/51.41 apply zenon_H27b. apply refl_equal. % 51.19/51.41 apply zenon_H278. apply sym_equal. exact zenon_H277. % 51.19/51.41 (* end of lemma zenon_L213_ *) % 51.19/51.41 assert (zenon_L214_ : ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e21) (e22)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H14 zenon_H1a8 zenon_H203 zenon_H277 zenon_H14e zenon_H27c. % 51.19/51.41 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 51.19/51.41 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e21) (e22)) = (op2 (e21) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H27c. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H188. % 51.19/51.41 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 51.19/51.41 cut (((op2 (e21) (e23)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 51.19/51.41 congruence. % 51.19/51.41 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e21) (e23)) = (op2 (e21) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H27d. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H14. % 51.19/51.41 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 51.19/51.41 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 51.19/51.41 congruence. % 51.19/51.41 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 51.19/51.41 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e20) = (op2 (e21) (e23)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H1a9. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H188. % 51.19/51.41 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 51.19/51.41 cut (((op2 (e21) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 51.19/51.41 congruence. % 51.19/51.41 exact (zenon_H27e zenon_H1a8). % 51.19/51.41 apply zenon_H189. apply refl_equal. % 51.19/51.41 apply zenon_H189. apply refl_equal. % 51.19/51.41 apply (zenon_L213_); trivial. % 51.19/51.41 apply zenon_H189. apply refl_equal. % 51.19/51.41 apply zenon_H189. apply refl_equal. % 51.19/51.41 (* end of lemma zenon_L214_ *) % 51.19/51.41 assert (zenon_L215_ : (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H27f zenon_H280 zenon_H281. % 51.19/51.41 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (e21) (e20)) = (op2 (e21) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H27f. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H280. % 51.19/51.41 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H282]. % 51.19/51.41 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H1aa. apply refl_equal. % 51.19/51.41 apply zenon_H282. apply sym_equal. exact zenon_H281. % 51.19/51.41 (* end of lemma zenon_L215_ *) % 51.19/51.41 assert (zenon_L216_ : (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e22)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H283 zenon_H284 zenon_H21d. % 51.19/51.41 cut (((op2 (e21) (e22)) = (e23)) = ((op2 (e21) (e22)) = (op2 (e23) (e22)))). % 51.19/51.41 intro zenon_D_pnotp. % 51.19/51.41 apply zenon_H283. % 51.19/51.41 rewrite <- zenon_D_pnotp. % 51.19/51.41 exact zenon_H284. % 51.19/51.41 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 51.19/51.41 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H182]. % 51.19/51.41 congruence. % 51.19/51.41 apply zenon_H182. apply refl_equal. % 51.19/51.41 apply zenon_H21e. apply sym_equal. exact zenon_H21d. % 51.19/51.41 (* end of lemma zenon_L216_ *) % 51.19/51.41 assert (zenon_L217_ : (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> False). % 51.19/51.41 do 0 intro. intros zenon_H285 zenon_H210 zenon_H14e zenon_H273 zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H26d zenon_H203 zenon_H19f zenon_H14 zenon_H19e zenon_H15e zenon_H1bd zenon_H1b1 zenon_H19b zenon_H187 zenon_H18e zenon_H27c zenon_H1f3 zenon_H280 zenon_H27f zenon_H195 zenon_H175 zenon_H1e7 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H283 zenon_H21d. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H277 | zenon_intro zenon_H286 ]. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1f4 ]. % 51.19/51.41 apply (zenon_L214_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f5 ]. % 51.19/51.41 apply (zenon_L145_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H186 | zenon_intro zenon_H1bc ]. % 51.19/51.41 apply (zenon_L124_); trivial. % 51.19/51.41 apply (zenon_L212_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H281 | zenon_intro zenon_H287 ]. % 51.19/51.41 apply (zenon_L215_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H17f | zenon_intro zenon_H284 ]. % 51.19/51.41 apply (zenon_L202_); trivial. % 51.19/51.41 apply (zenon_L216_); trivial. % 51.19/51.41 (* end of lemma zenon_L217_ *) % 51.19/51.41 assert (zenon_L218_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e20) = (e21))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.41 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H21d zenon_H283 zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H27f zenon_H280 zenon_H1f3 zenon_H27c zenon_H18e zenon_H187 zenon_H19b zenon_H1b1 zenon_H1bd zenon_H15e zenon_H19e zenon_H14 zenon_H19f zenon_H203 zenon_H26d zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H273 zenon_H210 zenon_H285 zenon_H1f7 zenon_H14e. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.41 apply (zenon_L194_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.41 apply (zenon_L212_); trivial. % 51.19/51.41 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.41 apply (zenon_L217_); trivial. % 51.19/51.41 apply (zenon_L149_); trivial. % 51.19/51.41 (* end of lemma zenon_L218_ *) % 51.19/51.41 assert (zenon_L219_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e21) = (e23))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H1f7 zenon_H285 zenon_H273 zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H26d zenon_H19f zenon_H19e zenon_H15e zenon_H1bd zenon_H1b1 zenon_H19b zenon_H187 zenon_H18e zenon_H27c zenon_H1f3 zenon_H280 zenon_H27f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H283 zenon_H21d zenon_H1ac zenon_H1fa zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.42 apply (zenon_L151_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.42 apply (zenon_L218_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L153_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L219_ *) % 51.19/51.42 assert (zenon_L220_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> (~((e20) = (e21))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H222 zenon_H21c zenon_H210 zenon_H14 zenon_H209 zenon_H1fa zenon_H1ac zenon_H283 zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H27f zenon_H280 zenon_H1f3 zenon_H27c zenon_H18e zenon_H187 zenon_H19b zenon_H1b1 zenon_H1bd zenon_H15e zenon_H19e zenon_H19f zenon_H26d zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H273 zenon_H285 zenon_H1fd zenon_H214 zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.19/51.42 apply (zenon_L192_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.19/51.42 apply (zenon_L155_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L219_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L220_ *) % 51.19/51.42 assert (zenon_L221_ : (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((e20) = (e21))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> False). % 51.19/51.42 do 0 intro. intros zenon_H230 zenon_H168 zenon_H203 zenon_H226 zenon_H225 zenon_H1a7 zenon_H16d zenon_H14e zenon_H1f7 zenon_H214 zenon_H1fd zenon_H285 zenon_H273 zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H26d zenon_H19f zenon_H15e zenon_H1bd zenon_H1b1 zenon_H19b zenon_H187 zenon_H18e zenon_H27c zenon_H1f3 zenon_H280 zenon_H27f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H283 zenon_H1ac zenon_H1fa zenon_H209 zenon_H14 zenon_H210 zenon_H222 zenon_H21b zenon_H21c. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H169 | zenon_intro zenon_H233 ]. % 51.19/51.42 apply (zenon_L118_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H17f | zenon_intro zenon_H234 ]. % 51.19/51.42 apply (zenon_L209_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H19e | zenon_intro zenon_H1d8 ]. % 51.19/51.42 apply (zenon_L220_); trivial. % 51.19/51.42 apply (zenon_L157_); trivial. % 51.19/51.42 (* end of lemma zenon_L221_ *) % 51.19/51.42 assert (zenon_L222_ : ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e21) = (e23))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H21c zenon_H21b zenon_H222 zenon_H1fa zenon_H1ac zenon_H283 zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H27f zenon_H280 zenon_H1f3 zenon_H27c zenon_H18e zenon_H187 zenon_H19b zenon_H1b1 zenon_H1bd zenon_H15e zenon_H19f zenon_H26d zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H273 zenon_H285 zenon_H1fd zenon_H214 zenon_H1f7 zenon_H16d zenon_H1a7 zenon_H225 zenon_H226 zenon_H168 zenon_H230 zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.42 apply (zenon_L151_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.42 apply (zenon_L221_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L153_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L222_ *) % 51.19/51.42 assert (zenon_L223_ : ((op2 (e22) (e20)) = (e21)) -> ((op2 (e22) (e20)) = (e22)) -> (~((e21) = (e22))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H26e zenon_H176 zenon_H288. % 51.19/51.42 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H170 | zenon_intro zenon_H171 ]. % 51.19/51.42 cut (((e22) = (e22)) = ((e21) = (e22))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H288. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H170. % 51.19/51.42 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.19/51.42 cut (((e22) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 51.19/51.42 congruence. % 51.19/51.42 cut (((op2 (e22) (e20)) = (e21)) = ((e22) = (e21))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H289. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H26e. % 51.19/51.42 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.42 cut (((op2 (e22) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H28a]. % 51.19/51.42 congruence. % 51.19/51.42 exact (zenon_H28a zenon_H176). % 51.19/51.42 apply zenon_H1f6. apply refl_equal. % 51.19/51.42 apply zenon_H171. apply refl_equal. % 51.19/51.42 apply zenon_H171. apply refl_equal. % 51.19/51.42 (* end of lemma zenon_L223_ *) % 51.19/51.42 assert (zenon_L224_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e22) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e20)) -> False). % 51.19/51.42 do 0 intro. intros zenon_H28b zenon_H203 zenon_H14e zenon_H1c9. % 51.19/51.42 cut (((op2 (e23) (e21)) = (e20)) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (e22) (e23)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H28b. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H203. % 51.19/51.42 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 51.19/51.42 cut (((op2 (e23) (e21)) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 51.19/51.42 congruence. % 51.19/51.42 elim (classic ((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [ zenon_intro zenon_H27a | zenon_intro zenon_H27b ]. % 51.19/51.42 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e21)) = (op2 (e23) (op2 (e23) (e23))))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H279. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H27a. % 51.19/51.42 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 51.19/51.42 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 51.19/51.42 congruence. % 51.19/51.42 apply (zenon_L112_); trivial. % 51.19/51.42 apply zenon_H27b. apply refl_equal. % 51.19/51.42 apply zenon_H27b. apply refl_equal. % 51.19/51.42 apply zenon_H1ca. apply sym_equal. exact zenon_H1c9. % 51.19/51.42 (* end of lemma zenon_L224_ *) % 51.19/51.42 assert (zenon_L225_ : (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e23)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H28c zenon_H14 zenon_H1a8 zenon_H203 zenon_H1c9 zenon_H14e. % 51.19/51.42 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H28c. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H14. % 51.19/51.42 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 51.19/51.42 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 51.19/51.42 congruence. % 51.19/51.42 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H188 | zenon_intro zenon_H189 ]. % 51.19/51.42 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e20) = (op2 (e21) (e23)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H1a9. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H188. % 51.19/51.42 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 51.19/51.42 cut (((op2 (e21) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 51.19/51.42 congruence. % 51.19/51.42 exact (zenon_H27e zenon_H1a8). % 51.19/51.42 apply zenon_H189. apply refl_equal. % 51.19/51.42 apply zenon_H189. apply refl_equal. % 51.19/51.42 apply (zenon_L224_); trivial. % 51.19/51.42 (* end of lemma zenon_L225_ *) % 51.19/51.42 assert (zenon_L226_ : ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1e7 zenon_H1e6 zenon_H1bd zenon_H1bc zenon_H203 zenon_H26e zenon_H26d zenon_H21d zenon_H175 zenon_H195. % 51.19/51.42 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.42 apply (zenon_L140_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.42 apply (zenon_L134_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.42 apply (zenon_L204_); trivial. % 51.19/51.42 apply (zenon_L201_); trivial. % 51.19/51.42 (* end of lemma zenon_L226_ *) % 51.19/51.42 assert (zenon_L227_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1f3 zenon_H1c9 zenon_H28c zenon_H14e zenon_H187 zenon_H14 zenon_H15e zenon_H1e7 zenon_H1e6 zenon_H1bd zenon_H203 zenon_H26e zenon_H26d zenon_H21d zenon_H175 zenon_H195. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1f4 ]. % 51.19/51.42 apply (zenon_L225_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f5 ]. % 51.19/51.42 apply (zenon_L145_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H186 | zenon_intro zenon_H1bc ]. % 51.19/51.42 apply (zenon_L124_); trivial. % 51.19/51.42 apply (zenon_L226_); trivial. % 51.19/51.42 (* end of lemma zenon_L227_ *) % 51.19/51.42 assert (zenon_L228_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H1d7 zenon_H195 zenon_H175 zenon_H21d zenon_H26d zenon_H26e zenon_H203 zenon_H1bd zenon_H1e6 zenon_H15e zenon_H14 zenon_H187 zenon_H28c zenon_H1c9 zenon_H1f3 zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.42 apply (zenon_L132_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.42 apply (zenon_L205_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L227_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L228_ *) % 51.19/51.42 assert (zenon_L229_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> (~((e20) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H222 zenon_H21c zenon_H210 zenon_H209 zenon_H205 zenon_H1fd zenon_H214 zenon_H1f3 zenon_H1c9 zenon_H28c zenon_H187 zenon_H14 zenon_H15e zenon_H1e6 zenon_H1bd zenon_H203 zenon_H26e zenon_H26d zenon_H175 zenon_H195 zenon_H1d7 zenon_H1ac zenon_H1fa zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.19/51.42 apply (zenon_L192_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.19/51.42 apply (zenon_L155_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L228_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L229_ *) % 51.19/51.42 assert (zenon_L230_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H22f zenon_H16f zenon_H16d zenon_H1a7 zenon_H1f7 zenon_H1fa zenon_H1ac zenon_H1d7 zenon_H195 zenon_H175 zenon_H26d zenon_H26e zenon_H203 zenon_H1bd zenon_H1e6 zenon_H15e zenon_H14 zenon_H187 zenon_H28c zenon_H1f3 zenon_H214 zenon_H1fd zenon_H205 zenon_H209 zenon_H21c zenon_H222 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.42 apply (zenon_L129_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.42 apply (zenon_L130_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L229_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L230_ *) % 51.19/51.42 assert (zenon_L231_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> (~((e20) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H222 zenon_H21c zenon_H205 zenon_H1fd zenon_H214 zenon_H1f3 zenon_H28c zenon_H187 zenon_H15e zenon_H1e6 zenon_H1bd zenon_H26e zenon_H26d zenon_H175 zenon_H195 zenon_H1d7 zenon_H1ac zenon_H1fa zenon_H1f7 zenon_H1a7 zenon_H16d zenon_H16f zenon_H22f zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.42 apply (zenon_L151_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.42 apply (zenon_L230_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L153_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L231_ *) % 51.19/51.42 assert (zenon_L232_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((e21) = (e22))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H28d zenon_H164 zenon_H168 zenon_H28e zenon_H15d zenon_H288 zenon_H222 zenon_H205 zenon_H1fd zenon_H214 zenon_H1f3 zenon_H28c zenon_H187 zenon_H15e zenon_H1e6 zenon_H1bd zenon_H26e zenon_H26d zenon_H195 zenon_H1d7 zenon_H1ac zenon_H1fa zenon_H1f7 zenon_H1a7 zenon_H16d zenon_H16f zenon_H22f zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.19/51.42 apply (zenon_L116_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.19/51.42 apply (zenon_L117_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.19/51.42 apply (zenon_L118_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.19/51.42 apply (zenon_L116_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.19/51.42 apply (zenon_L120_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.19/51.42 apply (zenon_L223_); trivial. % 51.19/51.42 apply (zenon_L231_); trivial. % 51.19/51.42 (* end of lemma zenon_L232_ *) % 51.19/51.42 assert (zenon_L233_ : ((op2 (e20) (e22)) = (e20)) -> ((op2 (e20) (e22)) = (e21)) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H156 zenon_H293 zenon_H210. % 51.19/51.42 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H211 | zenon_intro zenon_H1f6 ]. % 51.19/51.42 cut (((e21) = (e21)) = ((e20) = (e21))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H210. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H211. % 51.19/51.42 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.42 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 51.19/51.42 congruence. % 51.19/51.42 cut (((op2 (e20) (e22)) = (e20)) = ((e21) = (e20))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H212. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H156. % 51.19/51.42 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.42 cut (((op2 (e20) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 51.19/51.42 congruence. % 51.19/51.42 exact (zenon_H294 zenon_H293). % 51.19/51.42 apply zenon_H16c. apply refl_equal. % 51.19/51.42 apply zenon_H1f6. apply refl_equal. % 51.19/51.42 apply zenon_H1f6. apply refl_equal. % 51.19/51.42 (* end of lemma zenon_L233_ *) % 51.19/51.42 assert (zenon_L234_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e23)) = (e21)) -> False). % 51.19/51.42 do 0 intro. intros zenon_H195 zenon_H14e zenon_H295. % 51.19/51.42 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H195. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H14e. % 51.19/51.42 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.42 cut (((e21) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 51.19/51.42 congruence. % 51.19/51.42 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H297 | zenon_intro zenon_H298 ]. % 51.19/51.42 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e21) = (op2 (e20) (e23)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H296. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H297. % 51.19/51.42 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H298]. % 51.19/51.42 cut (((op2 (e20) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H299]. % 51.19/51.42 congruence. % 51.19/51.42 exact (zenon_H299 zenon_H295). % 51.19/51.42 apply zenon_H298. apply refl_equal. % 51.19/51.42 apply zenon_H298. apply refl_equal. % 51.19/51.42 apply zenon_H197. apply refl_equal. % 51.19/51.42 (* end of lemma zenon_L234_ *) % 51.19/51.42 assert (zenon_L235_ : (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1ec zenon_H14e zenon_H29a. % 51.19/51.42 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H1ec. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H14e. % 51.19/51.42 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.19/51.42 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 51.19/51.42 congruence. % 51.19/51.42 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H18f | zenon_intro zenon_H190 ]. % 51.19/51.42 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e21) = (op2 (e22) (e23)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H29b. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H18f. % 51.19/51.42 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 51.19/51.42 cut (((op2 (e22) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H29c]. % 51.19/51.42 congruence. % 51.19/51.42 exact (zenon_H29c zenon_H29a). % 51.19/51.42 apply zenon_H190. apply refl_equal. % 51.19/51.42 apply zenon_H190. apply refl_equal. % 51.19/51.42 apply zenon_H197. apply refl_equal. % 51.19/51.42 (* end of lemma zenon_L235_ *) % 51.19/51.42 assert (zenon_L236_ : (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H29d zenon_H266 zenon_H254 zenon_H18e zenon_H15e zenon_H24b zenon_H209 zenon_H14 zenon_H23c zenon_H21c zenon_H21b zenon_H175 zenon_H1d7 zenon_H23b zenon_H1a8 zenon_H240 zenon_H1ec zenon_H14e zenon_H244 zenon_H245. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H29d); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H29e ]. % 51.19/51.42 apply (zenon_L198_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H29e); [ zenon_intro zenon_H29a | zenon_intro zenon_H29f ]. % 51.19/51.42 apply (zenon_L235_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H29f); [ zenon_intro zenon_H18d | zenon_intro zenon_H1e7 ]. % 51.19/51.42 apply (zenon_L125_); trivial. % 51.19/51.42 apply (zenon_L174_); trivial. % 51.19/51.42 (* end of lemma zenon_L236_ *) % 51.19/51.42 assert (zenon_L237_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H22f zenon_H195 zenon_H187 zenon_H16f zenon_H19b zenon_H245 zenon_H244 zenon_H1ec zenon_H240 zenon_H23b zenon_H1d7 zenon_H175 zenon_H21b zenon_H21c zenon_H23c zenon_H14 zenon_H209 zenon_H24b zenon_H15e zenon_H18e zenon_H29d zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.42 apply (zenon_L183_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.42 apply (zenon_L236_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L198_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L237_ *) % 51.19/51.42 assert (zenon_L238_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H22f zenon_H16f zenon_H245 zenon_H244 zenon_H1e7 zenon_H1ec zenon_H1cc zenon_H1cd zenon_H1e6 zenon_H175 zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.42 apply (zenon_L129_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.42 apply (zenon_L177_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L198_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L238_ *) % 51.19/51.42 assert (zenon_L239_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H21f zenon_H1fd zenon_H217 zenon_H29d zenon_H18e zenon_H15e zenon_H24b zenon_H209 zenon_H14 zenon_H23c zenon_H21b zenon_H1d7 zenon_H23b zenon_H240 zenon_H19b zenon_H187 zenon_H195 zenon_H22f zenon_H16f zenon_H245 zenon_H244 zenon_H1e7 zenon_H1ec zenon_H1cc zenon_H1e6 zenon_H175 zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H220 ]. % 51.19/51.42 apply (zenon_L151_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H218 | zenon_intro zenon_H221 ]. % 51.19/51.42 apply (zenon_L156_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H21c | zenon_intro zenon_H1cd ]. % 51.19/51.42 apply (zenon_L237_); trivial. % 51.19/51.42 apply (zenon_L238_); trivial. % 51.19/51.42 (* end of lemma zenon_L239_ *) % 51.19/51.42 assert (zenon_L240_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> ((op2 (e21) (e23)) = (e20)) -> (~((e20) = (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H205 zenon_H1a8 zenon_H210 zenon_H254 zenon_H266 zenon_H175 zenon_H1e6 zenon_H1cc zenon_H1ec zenon_H244 zenon_H245 zenon_H16f zenon_H22f zenon_H195 zenon_H187 zenon_H19b zenon_H240 zenon_H23b zenon_H1d7 zenon_H21b zenon_H23c zenon_H14 zenon_H209 zenon_H24b zenon_H15e zenon_H18e zenon_H29d zenon_H217 zenon_H1fd zenon_H21f zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.42 apply (zenon_L132_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.42 apply (zenon_L184_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L239_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L240_ *) % 51.19/51.42 assert (zenon_L241_ : (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1f7 zenon_H21f zenon_H1fd zenon_H217 zenon_H29d zenon_H18e zenon_H15e zenon_H24b zenon_H209 zenon_H14 zenon_H23c zenon_H21b zenon_H1d7 zenon_H23b zenon_H240 zenon_H19b zenon_H187 zenon_H195 zenon_H22f zenon_H16f zenon_H245 zenon_H244 zenon_H1ec zenon_H1cc zenon_H1e6 zenon_H175 zenon_H205 zenon_H1ac zenon_H1fa zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.42 apply (zenon_L183_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.42 apply (zenon_L240_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L198_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L241_ *) % 51.19/51.42 assert (zenon_L242_ : ((op2 (e22) (e20)) = (e20)) -> ((op2 (e22) (e20)) = (e23)) -> (~((e20) = (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H266 zenon_H252 zenon_H205. % 51.19/51.42 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.42 cut (((e23) = (e23)) = ((e20) = (e23))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H205. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H1ad. % 51.19/51.42 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.42 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 51.19/51.42 congruence. % 51.19/51.42 cut (((op2 (e22) (e20)) = (e20)) = ((e23) = (e20))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H206. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H266. % 51.19/51.42 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.42 cut (((op2 (e22) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 51.19/51.42 congruence. % 51.19/51.42 exact (zenon_H2a0 zenon_H252). % 51.19/51.42 apply zenon_H16c. apply refl_equal. % 51.19/51.42 apply zenon_H14c. apply refl_equal. % 51.19/51.42 apply zenon_H14c. apply refl_equal. % 51.19/51.42 (* end of lemma zenon_L242_ *) % 51.19/51.42 assert (zenon_L243_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H205 zenon_H245 zenon_H244 zenon_H1ec zenon_H1cc zenon_H1a8 zenon_H1cd zenon_H1e6 zenon_H175 zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.42 apply (zenon_L132_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.42 apply (zenon_L184_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L177_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L243_ *) % 51.19/51.42 assert (zenon_L244_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e21) = (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H22f zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H1f7 zenon_H175 zenon_H1e6 zenon_H1cd zenon_H1cc zenon_H1ec zenon_H244 zenon_H245 zenon_H205 zenon_H1ac zenon_H1fa zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.42 apply (zenon_L183_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.42 apply (zenon_L243_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L198_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L244_ *) % 51.19/51.42 assert (zenon_L245_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e20) (e20)) = (e21)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e20) = (e23))) -> ((op2 (e20) (e22)) = (e20)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H28d zenon_H15d zenon_H164 zenon_H168 zenon_H258 zenon_H210 zenon_H14e zenon_H254 zenon_H266 zenon_H1fa zenon_H245 zenon_H1ec zenon_H1cc zenon_H1e6 zenon_H1f7 zenon_H16f zenon_H22f zenon_H21f zenon_H1fd zenon_H217 zenon_H29d zenon_H24b zenon_H209 zenon_H23c zenon_H21b zenon_H1d7 zenon_H240 zenon_H237 zenon_H259 zenon_H205 zenon_H156 zenon_H19b zenon_H1ac zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.19/51.42 apply (zenon_L116_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.19/51.42 apply (zenon_L117_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.19/51.42 apply (zenon_L118_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.19/51.42 apply (zenon_L166_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.19/51.42 apply (zenon_L166_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.19/51.42 apply (zenon_L241_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.19/51.42 apply (zenon_L242_); trivial. % 51.19/51.42 apply (zenon_L244_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.19/51.42 apply (zenon_L193_); trivial. % 51.19/51.42 apply (zenon_L194_); trivial. % 51.19/51.42 (* end of lemma zenon_L245_ *) % 51.19/51.42 assert (zenon_L246_ : (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H26d zenon_H14 zenon_H2a1 zenon_H14e. % 51.19/51.42 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H26d. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H14. % 51.19/51.42 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 51.19/51.42 cut (((e20) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 51.19/51.42 congruence. % 51.19/51.42 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H246 | zenon_intro zenon_H247 ]. % 51.19/51.42 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e20) = (op2 (e21) (e21)))). % 51.19/51.42 intro zenon_D_pnotp. % 51.19/51.42 apply zenon_H2a2. % 51.19/51.42 rewrite <- zenon_D_pnotp. % 51.19/51.42 exact zenon_H246. % 51.19/51.42 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 51.19/51.42 cut (((op2 (e21) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 51.19/51.42 congruence. % 51.19/51.42 exact (zenon_H2a3 zenon_H2a1). % 51.19/51.42 apply zenon_H247. apply refl_equal. % 51.19/51.42 apply zenon_H247. apply refl_equal. % 51.19/51.42 apply (zenon_L112_); trivial. % 51.19/51.42 (* end of lemma zenon_L246_ *) % 51.19/51.42 assert (zenon_L247_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e22)) = (e20)) -> ((op2 (e23) (e21)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H22f zenon_H16f zenon_H175 zenon_H27c zenon_H277 zenon_H203 zenon_H14 zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.42 apply (zenon_L129_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.42 apply (zenon_L214_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L198_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L247_ *) % 51.19/51.42 assert (zenon_L248_ : (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e21) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e21))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e23)) -> False). % 51.19/51.42 do 0 intro. intros zenon_H285 zenon_H27c zenon_H203 zenon_H1a8 zenon_H14 zenon_H280 zenon_H27f zenon_H14e zenon_H1f7 zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H22f zenon_H16f zenon_H205 zenon_H266 zenon_H254 zenon_H210 zenon_H1ac zenon_H1fa zenon_H283 zenon_H21d. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H285); [ zenon_intro zenon_H277 | zenon_intro zenon_H286 ]. % 51.19/51.42 apply (zenon_L214_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H286); [ zenon_intro zenon_H281 | zenon_intro zenon_H287 ]. % 51.19/51.42 apply (zenon_L215_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H287); [ zenon_intro zenon_H17f | zenon_intro zenon_H284 ]. % 51.19/51.42 apply (zenon_L203_); trivial. % 51.19/51.42 apply (zenon_L216_); trivial. % 51.19/51.42 (* end of lemma zenon_L248_ *) % 51.19/51.42 assert (zenon_L249_ : ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H21d zenon_H283 zenon_H1fa zenon_H1ac zenon_H205 zenon_H16f zenon_H22f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H1f7 zenon_H27f zenon_H280 zenon_H14 zenon_H203 zenon_H27c zenon_H285 zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.42 apply (zenon_L129_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.42 apply (zenon_L248_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L198_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L249_ *) % 51.19/51.42 assert (zenon_L250_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> (~((e20) = (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H222 zenon_H21c zenon_H210 zenon_H254 zenon_H266 zenon_H285 zenon_H27c zenon_H203 zenon_H14 zenon_H280 zenon_H27f zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H22f zenon_H16f zenon_H205 zenon_H1ac zenon_H1fa zenon_H283 zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.19/51.42 apply (zenon_L192_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.19/51.42 apply (zenon_L152_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L249_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L250_ *) % 51.19/51.42 assert (zenon_L251_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H1f7 zenon_H283 zenon_H1fa zenon_H1ac zenon_H205 zenon_H16f zenon_H22f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H27f zenon_H280 zenon_H27c zenon_H285 zenon_H266 zenon_H254 zenon_H21c zenon_H222 zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.42 apply (zenon_L151_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.42 apply (zenon_L250_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.42 apply (zenon_L153_); trivial. % 51.19/51.42 apply (zenon_L154_); trivial. % 51.19/51.42 (* end of lemma zenon_L251_ *) % 51.19/51.42 assert (zenon_L252_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H1fa zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H1ac zenon_H19b zenon_H205 zenon_H1d8 zenon_H1d7 zenon_H1ec zenon_H1cc zenon_H1a8 zenon_H1cd zenon_H1e6 zenon_H175 zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.42 apply (zenon_L194_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.42 apply (zenon_L184_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L144_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L252_ *) % 51.19/51.42 assert (zenon_L253_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e23) (e22)) = (e22)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H222 zenon_H1e6 zenon_H1cc zenon_H1d8 zenon_H19b zenon_H187 zenon_H18e zenon_H15e zenon_H283 zenon_H1fa zenon_H1ac zenon_H210 zenon_H254 zenon_H266 zenon_H205 zenon_H16f zenon_H22f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H27f zenon_H280 zenon_H14 zenon_H1a8 zenon_H203 zenon_H27c zenon_H285 zenon_H1f7 zenon_H14e. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.19/51.42 apply (zenon_L252_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.19/51.42 apply (zenon_L152_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.19/51.42 apply (zenon_L248_); trivial. % 51.19/51.42 apply (zenon_L149_); trivial. % 51.19/51.42 (* end of lemma zenon_L253_ *) % 51.19/51.42 assert (zenon_L254_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e21))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H24e zenon_H209 zenon_H1fd zenon_H214 zenon_H14e zenon_H1f7 zenon_H285 zenon_H27c zenon_H203 zenon_H1a8 zenon_H280 zenon_H27f zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H22f zenon_H16f zenon_H205 zenon_H266 zenon_H254 zenon_H210 zenon_H1ac zenon_H1fa zenon_H283 zenon_H18e zenon_H187 zenon_H19b zenon_H1cc zenon_H1e6 zenon_H222 zenon_H15e zenon_H14 zenon_H195. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.19/51.42 apply (zenon_L251_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.19/51.42 apply (zenon_L162_); trivial. % 51.19/51.42 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.19/51.42 apply (zenon_L253_); trivial. % 51.19/51.42 apply (zenon_L126_); trivial. % 51.19/51.42 (* end of lemma zenon_L254_ *) % 51.19/51.42 assert (zenon_L255_ : ((op2 (e22) (e20)) = (e20)) -> ((op2 (e22) (e20)) = (e22)) -> (~((e20) = (e22))) -> False). % 51.19/51.42 do 0 intro. intros zenon_H266 zenon_H176 zenon_H16f. % 51.19/51.42 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H170 | zenon_intro zenon_H171 ]. % 51.19/51.42 cut (((e22) = (e22)) = ((e20) = (e22))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H16f. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H170. % 51.19/51.43 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.19/51.43 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 51.19/51.43 congruence. % 51.19/51.43 cut (((op2 (e22) (e20)) = (e20)) = ((e22) = (e20))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H172. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H266. % 51.19/51.43 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.43 cut (((op2 (e22) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H28a]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H28a zenon_H176). % 51.19/51.43 apply zenon_H16c. apply refl_equal. % 51.19/51.43 apply zenon_H171. apply refl_equal. % 51.19/51.43 apply zenon_H171. apply refl_equal. % 51.19/51.43 (* end of lemma zenon_L255_ *) % 51.19/51.43 assert (zenon_L256_ : ((op2 (e22) (e20)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((e20) = (e21))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H266 zenon_H26e zenon_H210. % 51.19/51.43 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H211 | zenon_intro zenon_H1f6 ]. % 51.19/51.43 cut (((e21) = (e21)) = ((e20) = (e21))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H210. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H211. % 51.19/51.43 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.43 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 51.19/51.43 congruence. % 51.19/51.43 cut (((op2 (e22) (e20)) = (e20)) = ((e21) = (e20))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H212. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H266. % 51.19/51.43 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.43 cut (((op2 (e22) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2a4]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H2a4 zenon_H26e). % 51.19/51.43 apply zenon_H16c. apply refl_equal. % 51.19/51.43 apply zenon_H1f6. apply refl_equal. % 51.19/51.43 apply zenon_H1f6. apply refl_equal. % 51.19/51.43 (* end of lemma zenon_L256_ *) % 51.19/51.43 assert (zenon_L257_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((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 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (~((e20) = (e21))) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2a5 zenon_H259 zenon_H240 zenon_H21b zenon_H23c zenon_H24b zenon_H29d zenon_H21f zenon_H245 zenon_H258 zenon_H217 zenon_H266 zenon_H28d zenon_H164 zenon_H168 zenon_H28e zenon_H15d zenon_H24e zenon_H18e zenon_H187 zenon_H19b zenon_H1cc zenon_H1e6 zenon_H15e zenon_H26d zenon_H2a6 zenon_H214 zenon_H1fd zenon_H1f7 zenon_H283 zenon_H1fa zenon_H1ac zenon_H205 zenon_H16f zenon_H22f zenon_H1ec zenon_H267 zenon_H1d7 zenon_H27f zenon_H27c zenon_H285 zenon_H254 zenon_H222 zenon_H209 zenon_H14 zenon_H25f zenon_H2a7 zenon_H210 zenon_H156 zenon_H195 zenon_H14e. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.19/51.43 apply (zenon_L245_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.19/51.43 apply (zenon_L196_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.19/51.43 apply (zenon_L116_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.19/51.43 apply (zenon_L117_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.19/51.43 apply (zenon_L118_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.19/51.43 apply (zenon_L116_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H16d | zenon_intro zenon_H2ac ]. % 51.19/51.43 apply (zenon_L120_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H2a1 | zenon_intro zenon_H2ad ]. % 51.19/51.43 apply (zenon_L246_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H277 | zenon_intro zenon_H1a8 ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.43 apply (zenon_L151_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.43 apply (zenon_L247_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.43 apply (zenon_L153_); trivial. % 51.19/51.43 apply (zenon_L154_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.43 apply (zenon_L151_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.43 apply (zenon_L254_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.43 apply (zenon_L153_); trivial. % 51.19/51.43 apply (zenon_L154_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.19/51.43 apply (zenon_L255_); trivial. % 51.19/51.43 apply (zenon_L251_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.19/51.43 apply (zenon_L256_); trivial. % 51.19/51.43 apply (zenon_L156_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.19/51.43 apply (zenon_L233_); trivial. % 51.19/51.43 apply (zenon_L234_); trivial. % 51.19/51.43 (* end of lemma zenon_L257_ *) % 51.19/51.43 assert (zenon_L258_ : (((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)) = (op2 (e22) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((e21) = (e22))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e20)) -> (~((e20) = (e21))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e21))\/((op2 (e23) (e20)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> (((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 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (((op2 (e22) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e22) (e23)) = (e23))))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2ae zenon_H157 zenon_H1b1 zenon_H19f zenon_H273 zenon_H225 zenon_H230 zenon_H262 zenon_H2af zenon_H22e zenon_H180 zenon_H22b zenon_H1a7 zenon_H1bd zenon_H28c zenon_H1f3 zenon_H288 zenon_H195 zenon_H156 zenon_H210 zenon_H2a7 zenon_H25f zenon_H209 zenon_H222 zenon_H254 zenon_H285 zenon_H27c zenon_H27f zenon_H1d7 zenon_H267 zenon_H1ec zenon_H22f zenon_H16f zenon_H205 zenon_H1ac zenon_H1fa zenon_H283 zenon_H1f7 zenon_H214 zenon_H2a6 zenon_H26d zenon_H15e zenon_H1e6 zenon_H1cc zenon_H19b zenon_H187 zenon_H18e zenon_H24e zenon_H15d zenon_H28e zenon_H168 zenon_H164 zenon_H28d zenon_H217 zenon_H258 zenon_H245 zenon_H21f zenon_H29d zenon_H24b zenon_H23c zenon_H21b zenon_H240 zenon_H259 zenon_H2a5 zenon_H1fd zenon_H14 zenon_H14e. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H13c | zenon_intro zenon_H2b0 ]. % 51.19/51.43 apply (zenon_L114_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H16d | zenon_intro zenon_H2b1 ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.19/51.43 apply (zenon_L116_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.19/51.43 apply (zenon_L117_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.19/51.43 apply (zenon_L118_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.19/51.43 apply (zenon_L116_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.19/51.43 apply (zenon_L120_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.19/51.43 apply (zenon_L165_); trivial. % 51.19/51.43 apply (zenon_L195_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.19/51.43 apply (zenon_L196_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.19/51.43 apply (zenon_L116_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.19/51.43 apply (zenon_L117_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.19/51.43 apply (zenon_L118_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.19/51.43 apply (zenon_L116_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.19/51.43 apply (zenon_L120_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.19/51.43 apply (zenon_L165_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H176 | zenon_intro zenon_H2b2 ]. % 51.19/51.43 apply (zenon_L197_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H226 | zenon_intro zenon_H2b3 ]. % 51.19/51.43 apply (zenon_L222_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H19e | zenon_intro zenon_H18d ]. % 51.19/51.43 apply (zenon_L220_); trivial. % 51.19/51.43 apply (zenon_L125_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.19/51.43 apply (zenon_L232_); trivial. % 51.19/51.43 apply (zenon_L156_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.19/51.43 apply (zenon_L233_); trivial. % 51.19/51.43 apply (zenon_L234_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H266 | zenon_intro zenon_H1fe ]. % 51.19/51.43 apply (zenon_L257_); trivial. % 51.19/51.43 apply (zenon_L151_); trivial. % 51.19/51.43 (* end of lemma zenon_L258_ *) % 51.19/51.43 assert (zenon_L259_ : ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e20)) = (e21)) -> (~((e20) = (e21))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H13c zenon_H237 zenon_H210. % 51.19/51.43 elim (classic ((e21) = (e21))); [ zenon_intro zenon_H211 | zenon_intro zenon_H1f6 ]. % 51.19/51.43 cut (((e21) = (e21)) = ((e20) = (e21))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H210. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H211. % 51.19/51.43 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.43 cut (((e21) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 51.19/51.43 congruence. % 51.19/51.43 cut (((op2 (e20) (e20)) = (e20)) = ((e21) = (e20))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H212. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H13c. % 51.19/51.43 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.43 cut (((op2 (e20) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H2b4 zenon_H237). % 51.19/51.43 apply zenon_H16c. apply refl_equal. % 51.19/51.43 apply zenon_H1f6. apply refl_equal. % 51.19/51.43 apply zenon_H1f6. apply refl_equal. % 51.19/51.43 (* end of lemma zenon_L259_ *) % 51.19/51.43 assert (zenon_L260_ : ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e20)) = (e23)) -> (~((e20) = (e23))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H13c zenon_H238 zenon_H205. % 51.19/51.43 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.43 cut (((e23) = (e23)) = ((e20) = (e23))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H205. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H1ad. % 51.19/51.43 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.43 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 51.19/51.43 congruence. % 51.19/51.43 cut (((op2 (e20) (e20)) = (e20)) = ((e23) = (e20))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H206. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H13c. % 51.19/51.43 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.19/51.43 cut (((op2 (e20) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H23a zenon_H238). % 51.19/51.43 apply zenon_H16c. apply refl_equal. % 51.19/51.43 apply zenon_H14c. apply refl_equal. % 51.19/51.43 apply zenon_H14c. apply refl_equal. % 51.19/51.43 (* end of lemma zenon_L260_ *) % 51.19/51.43 assert (zenon_L261_ : ((op2 (e20) (e21)) = (e21)) -> ((op2 (e20) (e21)) = (e23)) -> (~((e21) = (e23))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H25e zenon_H244 zenon_H1f7. % 51.19/51.43 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.19/51.43 cut (((e23) = (e23)) = ((e21) = (e23))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H1f7. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H1ad. % 51.19/51.43 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.19/51.43 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 51.19/51.43 congruence. % 51.19/51.43 cut (((op2 (e20) (e21)) = (e21)) = ((e23) = (e21))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H239. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H25e. % 51.19/51.43 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.19/51.43 cut (((op2 (e20) (e21)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H2b5 zenon_H244). % 51.19/51.43 apply zenon_H1f6. apply refl_equal. % 51.19/51.43 apply zenon_H14c. apply refl_equal. % 51.19/51.43 apply zenon_H14c. apply refl_equal. % 51.19/51.43 (* end of lemma zenon_L261_ *) % 51.19/51.43 assert (zenon_L262_ : (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2b6 zenon_H256 zenon_H21d. % 51.19/51.43 cut (((op2 (e20) (e22)) = (e23)) = ((op2 (e20) (e22)) = (op2 (e23) (e22)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2b6. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H256. % 51.19/51.43 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 51.19/51.43 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 51.19/51.43 congruence. % 51.19/51.43 apply zenon_H159. apply refl_equal. % 51.19/51.43 apply zenon_H21e. apply sym_equal. exact zenon_H21d. % 51.19/51.43 (* end of lemma zenon_L262_ *) % 51.19/51.43 assert (zenon_L263_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> False). % 51.19/51.43 do 0 intro. intros zenon_H24b zenon_H209 zenon_H14 zenon_H14e zenon_H23c zenon_H21c zenon_H21b zenon_H2b6 zenon_H256. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H208 | zenon_intro zenon_H24c ]. % 51.19/51.43 apply (zenon_L153_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H23d | zenon_intro zenon_H24d ]. % 51.19/51.43 apply (zenon_L168_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H21d ]. % 51.19/51.43 apply (zenon_L157_); trivial. % 51.19/51.43 apply (zenon_L262_); trivial. % 51.19/51.43 (* end of lemma zenon_L263_ *) % 51.19/51.43 assert (zenon_L264_ : (((op2 (op2 (e20) (e20)) (op2 (e20) (e20))) = (e20))/\(((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e21))/\(((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e22))/\((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e23))))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H1b0 zenon_H175 zenon_H256 zenon_H2b7. % 51.19/51.43 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_H1b3. zenon_intro zenon_H1b2. % 51.19/51.43 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b5. zenon_intro zenon_H1b4. % 51.19/51.43 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H1b7. zenon_intro zenon_H1b6. % 51.19/51.43 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.43 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2b7. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H1a0. % 51.19/51.43 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.43 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b8]. % 51.19/51.43 congruence. % 51.19/51.43 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (e23)) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2b8. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H1b6. % 51.19/51.43 cut (((e23) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b9]. % 51.19/51.43 cut (((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 51.19/51.43 congruence. % 51.19/51.43 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.19/51.43 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (op2 (e20) (e23)) (op2 (e20) (e23))) = (op2 (e22) (e22)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H1e9. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H1a0. % 51.19/51.43 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.19/51.43 cut (((op2 (e22) (e22)) = (op2 (op2 (e20) (e23)) (op2 (e20) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 51.19/51.43 congruence. % 51.19/51.43 apply (zenon_L139_); trivial. % 51.19/51.43 apply zenon_H1a1. apply refl_equal. % 51.19/51.43 apply zenon_H1a1. apply refl_equal. % 51.19/51.43 apply zenon_H2b9. apply sym_equal. exact zenon_H256. % 51.19/51.43 apply zenon_H1a1. apply refl_equal. % 51.19/51.43 apply zenon_H1a1. apply refl_equal. % 51.19/51.43 (* end of lemma zenon_L264_ *) % 51.19/51.43 assert (zenon_L265_ : (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2b7 zenon_H256 zenon_H175 zenon_H1cd zenon_H1a8 zenon_H1cc zenon_H1ec zenon_H1e7 zenon_H1d7 zenon_H1d8. % 51.19/51.43 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.43 apply (zenon_L264_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.43 apply (zenon_L142_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.43 apply (zenon_L143_); trivial. % 51.19/51.43 apply (zenon_L137_); trivial. % 51.19/51.43 (* end of lemma zenon_L265_ *) % 51.19/51.43 assert (zenon_L266_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H24e zenon_H1ac zenon_H16f zenon_H203 zenon_H1d7 zenon_H1e7 zenon_H1ec zenon_H1cc zenon_H1a8 zenon_H1cd zenon_H175 zenon_H256 zenon_H2b7 zenon_H15e zenon_H14 zenon_H195. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.19/51.43 apply (zenon_L192_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.19/51.43 apply (zenon_L162_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.19/51.43 apply (zenon_L265_); trivial. % 51.19/51.43 apply (zenon_L126_); trivial. % 51.19/51.43 (* end of lemma zenon_L266_ *) % 51.19/51.43 assert (zenon_L267_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H24e zenon_H1ac zenon_H210 zenon_H14e zenon_H209 zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1c9 zenon_H1cd zenon_H1bc zenon_H1bd zenon_H1e6 zenon_H175 zenon_H1e7 zenon_H15e zenon_H14 zenon_H195. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.19/51.43 apply (zenon_L192_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.19/51.43 apply (zenon_L163_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.19/51.43 apply (zenon_L146_); trivial. % 51.19/51.43 apply (zenon_L126_); trivial. % 51.19/51.43 (* end of lemma zenon_L267_ *) % 51.19/51.43 assert (zenon_L268_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H1f3 zenon_H2b7 zenon_H256 zenon_H1ec zenon_H203 zenon_H187 zenon_H24e zenon_H1ac zenon_H210 zenon_H14e zenon_H209 zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1c9 zenon_H1cd zenon_H1bd zenon_H1e6 zenon_H175 zenon_H1e7 zenon_H15e zenon_H14 zenon_H195. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1f3); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1f4 ]. % 51.19/51.43 apply (zenon_L266_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H1f5 ]. % 51.19/51.43 apply (zenon_L145_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_H186 | zenon_intro zenon_H1bc ]. % 51.19/51.43 apply (zenon_L124_); trivial. % 51.19/51.43 apply (zenon_L267_); trivial. % 51.19/51.43 (* end of lemma zenon_L268_ *) % 51.19/51.43 assert (zenon_L269_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H22f zenon_H18e zenon_H19b zenon_H195 zenon_H14 zenon_H15e zenon_H1e7 zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H209 zenon_H1ac zenon_H24e zenon_H187 zenon_H203 zenon_H1ec zenon_H256 zenon_H2b7 zenon_H1f3 zenon_H14e zenon_H210. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.43 apply (zenon_L183_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.43 apply (zenon_L266_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.43 apply (zenon_L268_); trivial. % 51.19/51.43 apply (zenon_L154_); trivial. % 51.19/51.43 (* end of lemma zenon_L269_ *) % 51.19/51.43 assert (zenon_L270_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H1f3 zenon_H2b7 zenon_H256 zenon_H1ec zenon_H187 zenon_H24e zenon_H1ac zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1cd zenon_H1bd zenon_H1e6 zenon_H175 zenon_H1e7 zenon_H15e zenon_H195 zenon_H19b zenon_H18e zenon_H22f zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.43 apply (zenon_L151_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.43 apply (zenon_L269_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.43 apply (zenon_L153_); trivial. % 51.19/51.43 apply (zenon_L154_); trivial. % 51.19/51.43 (* end of lemma zenon_L270_ *) % 51.19/51.43 assert (zenon_L271_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H21f zenon_H217 zenon_H1d8 zenon_H21b zenon_H1f3 zenon_H2b7 zenon_H256 zenon_H1ec zenon_H187 zenon_H24e zenon_H1ac zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H175 zenon_H1e7 zenon_H15e zenon_H195 zenon_H19b zenon_H18e zenon_H22f zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H220 ]. % 51.19/51.43 apply (zenon_L151_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H218 | zenon_intro zenon_H221 ]. % 51.19/51.43 apply (zenon_L156_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H21c | zenon_intro zenon_H1cd ]. % 51.19/51.43 apply (zenon_L157_); trivial. % 51.19/51.43 apply (zenon_L270_); trivial. % 51.19/51.43 (* end of lemma zenon_L271_ *) % 51.19/51.43 assert (zenon_L272_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> ((op2 (e21) (e23)) = (e20)) -> (~((e20) = (e21))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H1fa zenon_H205 zenon_H1a8 zenon_H210 zenon_H14 zenon_H209 zenon_H22f zenon_H18e zenon_H19b zenon_H195 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H1ac zenon_H24e zenon_H187 zenon_H1ec zenon_H256 zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H21f zenon_H1f7 zenon_H14e. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.43 apply (zenon_L132_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.43 apply (zenon_L184_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.43 apply (zenon_L271_); trivial. % 51.19/51.43 apply (zenon_L149_); trivial. % 51.19/51.43 (* end of lemma zenon_L272_ *) % 51.19/51.43 assert (zenon_L273_ : ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e21))) -> ((op2 (e21) (e23)) = (e20)) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H14e zenon_H1f7 zenon_H21f zenon_H217 zenon_H1d8 zenon_H21b zenon_H1f3 zenon_H2b7 zenon_H256 zenon_H1ec zenon_H24e zenon_H1ac zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H19b zenon_H22f zenon_H209 zenon_H210 zenon_H1a8 zenon_H205 zenon_H1fa zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.19/51.43 apply (zenon_L272_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.19/51.43 apply (zenon_L124_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.19/51.43 apply (zenon_L125_); trivial. % 51.19/51.43 apply (zenon_L126_); trivial. % 51.19/51.43 (* end of lemma zenon_L273_ *) % 51.19/51.43 assert (zenon_L274_ : (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2b7 zenon_H256 zenon_H175 zenon_H1bd zenon_H1bc zenon_H1cd zenon_H1c9 zenon_H1cc zenon_H1d7 zenon_H1d8. % 51.19/51.43 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.19/51.43 apply (zenon_L264_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.19/51.43 apply (zenon_L134_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.19/51.43 apply (zenon_L136_); trivial. % 51.19/51.43 apply (zenon_L137_); trivial. % 51.19/51.43 (* end of lemma zenon_L274_ *) % 51.19/51.43 assert (zenon_L275_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> False). % 51.19/51.43 do 0 intro. intros zenon_H21f zenon_H14 zenon_H1fd zenon_H14e zenon_H217 zenon_H21b zenon_H2b7 zenon_H256 zenon_H175 zenon_H1bd zenon_H1bc zenon_H1c9 zenon_H1cc zenon_H1d7 zenon_H1d8. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H220 ]. % 51.19/51.43 apply (zenon_L151_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H218 | zenon_intro zenon_H221 ]. % 51.19/51.43 apply (zenon_L156_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H21c | zenon_intro zenon_H1cd ]. % 51.19/51.43 apply (zenon_L157_); trivial. % 51.19/51.43 apply (zenon_L274_); trivial. % 51.19/51.43 (* end of lemma zenon_L275_ *) % 51.19/51.43 assert (zenon_L276_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H195 zenon_H15e zenon_H18e zenon_H187 zenon_H1fa zenon_H205 zenon_H209 zenon_H22f zenon_H19b zenon_H1e6 zenon_H214 zenon_H16f zenon_H1ac zenon_H24e zenon_H1ec zenon_H1f3 zenon_H1f7 zenon_H1d8 zenon_H1d7 zenon_H1cc zenon_H1bc zenon_H1bd zenon_H175 zenon_H256 zenon_H2b7 zenon_H21b zenon_H217 zenon_H1fd zenon_H14 zenon_H21f zenon_H14e zenon_H210. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.19/51.43 apply (zenon_L129_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.19/51.43 apply (zenon_L273_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.19/51.43 apply (zenon_L275_); trivial. % 51.19/51.43 apply (zenon_L154_); trivial. % 51.19/51.43 (* end of lemma zenon_L276_ *) % 51.19/51.43 assert (zenon_L277_ : (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e21))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H205 zenon_H1fa zenon_H210 zenon_H14 zenon_H209 zenon_H22f zenon_H18e zenon_H19b zenon_H195 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H1ac zenon_H24e zenon_H187 zenon_H1ec zenon_H256 zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H21f zenon_H1f7 zenon_H14e. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.19/51.43 apply (zenon_L194_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.19/51.43 apply (zenon_L276_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.19/51.43 apply (zenon_L271_); trivial. % 51.19/51.43 apply (zenon_L149_); trivial. % 51.19/51.43 (* end of lemma zenon_L277_ *) % 51.19/51.43 assert (zenon_L278_ : (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> ((op2 (e23) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e21))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2b6 zenon_H23c zenon_H24b zenon_H203 zenon_H14e zenon_H1f7 zenon_H21f zenon_H217 zenon_H21b zenon_H1f3 zenon_H2b7 zenon_H256 zenon_H1ec zenon_H187 zenon_H24e zenon_H1ac zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H175 zenon_H19b zenon_H18e zenon_H22f zenon_H209 zenon_H210 zenon_H1fa zenon_H205 zenon_H15e zenon_H14 zenon_H195. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.19/51.43 apply (zenon_L263_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.19/51.43 apply (zenon_L162_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.19/51.43 apply (zenon_L277_); trivial. % 51.19/51.43 apply (zenon_L126_); trivial. % 51.19/51.43 (* end of lemma zenon_L278_ *) % 51.19/51.43 assert (zenon_L279_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H195 zenon_H15e zenon_H205 zenon_H1fa zenon_H22f zenon_H18e zenon_H19b zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H1ac zenon_H24e zenon_H187 zenon_H1ec zenon_H256 zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H217 zenon_H21f zenon_H1f7 zenon_H24b zenon_H23c zenon_H2b6 zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.19/51.43 apply (zenon_L151_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.19/51.43 apply (zenon_L278_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.19/51.43 apply (zenon_L153_); trivial. % 51.19/51.43 apply (zenon_L154_); trivial. % 51.19/51.43 (* end of lemma zenon_L279_ *) % 51.19/51.43 assert (zenon_L280_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e21)) = (e21)) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((e22) = (e23))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H28d zenon_H15d zenon_H164 zenon_H168 zenon_H258 zenon_H13c zenon_H25e zenon_H210 zenon_H14e zenon_H14 zenon_H209 zenon_H2b6 zenon_H23c zenon_H24b zenon_H1f7 zenon_H21f zenon_H217 zenon_H21b zenon_H1f3 zenon_H2b7 zenon_H1ec zenon_H187 zenon_H24e zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H19b zenon_H18e zenon_H22f zenon_H1fa zenon_H205 zenon_H15e zenon_H195 zenon_H1ac. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.19/51.43 apply (zenon_L116_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.19/51.43 apply (zenon_L117_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.19/51.43 apply (zenon_L118_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.19/51.43 apply (zenon_L260_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.19/51.43 apply (zenon_L261_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.19/51.43 apply (zenon_L279_); trivial. % 51.19/51.43 apply (zenon_L132_); trivial. % 51.19/51.43 (* end of lemma zenon_L280_ *) % 51.19/51.43 assert (zenon_L281_ : (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e10) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2ba zenon_H2c zenon_H2bb zenon_H1c. % 51.19/51.43 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e10) (e11)) = (op1 (e10) (e13)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2ba. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H2c. % 51.19/51.43 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 51.19/51.43 cut (((e12) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2bc]. % 51.19/51.43 congruence. % 51.19/51.43 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 51.19/51.43 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e12) = (op1 (e10) (e11)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2bc. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H1f. % 51.19/51.43 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 51.19/51.43 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2bd]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H2bd zenon_H2bb). % 51.19/51.43 apply zenon_H20. apply refl_equal. % 51.19/51.43 apply zenon_H20. apply refl_equal. % 51.19/51.43 apply (zenon_L6_); trivial. % 51.19/51.43 (* end of lemma zenon_L281_ *) % 51.19/51.43 assert (zenon_L282_ : (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e10) (e12)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2be zenon_H2c zenon_H2bf zenon_H1c. % 51.19/51.43 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e10) (e12)) = (op1 (e10) (e13)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2be. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H2c. % 51.19/51.43 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 51.19/51.43 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2c0]. % 51.19/51.43 congruence. % 51.19/51.43 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 51.19/51.43 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e12) = (op1 (e10) (e12)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2c0. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H25. % 51.19/51.43 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 51.19/51.43 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2c1]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H2c1 zenon_H2bf). % 51.19/51.43 apply zenon_H26. apply refl_equal. % 51.19/51.43 apply zenon_H26. apply refl_equal. % 51.19/51.43 apply (zenon_L6_); trivial. % 51.19/51.43 (* end of lemma zenon_L282_ *) % 51.19/51.43 assert (zenon_L283_ : (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.43 do 0 intro. intros zenon_H10e zenon_H1c zenon_H2c2 zenon_H19. % 51.19/51.43 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H10e. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H1c. % 51.19/51.43 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 51.19/51.43 cut (((e10) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 51.19/51.43 congruence. % 51.19/51.43 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H7a | zenon_intro zenon_H7b ]. % 51.19/51.43 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e10) = (op1 (e11) (e11)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2c3. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H7a. % 51.19/51.43 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 51.19/51.43 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2c4]. % 51.19/51.43 congruence. % 51.19/51.43 exact (zenon_H2c4 zenon_H2c2). % 51.19/51.43 apply zenon_H7b. apply refl_equal. % 51.19/51.43 apply zenon_H7b. apply refl_equal. % 51.19/51.43 apply (zenon_L3_); trivial. % 51.19/51.43 (* end of lemma zenon_L283_ *) % 51.19/51.43 assert (zenon_L284_ : (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> False). % 51.19/51.43 do 0 intro. intros zenon_H2c5 zenon_H34 zenon_H2c6. % 51.19/51.43 cut (((op1 (e11) (e10)) = (e12)) = ((op1 (e11) (e10)) = (op1 (e11) (e11)))). % 51.19/51.43 intro zenon_D_pnotp. % 51.19/51.43 apply zenon_H2c5. % 51.19/51.43 rewrite <- zenon_D_pnotp. % 51.19/51.43 exact zenon_H34. % 51.19/51.43 cut (((e12) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 51.19/51.43 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 51.19/51.43 congruence. % 51.19/51.43 apply zenon_Hf7. apply refl_equal. % 51.19/51.43 apply zenon_H2c7. apply sym_equal. exact zenon_H2c6. % 51.19/51.43 (* end of lemma zenon_L284_ *) % 51.19/51.43 assert (zenon_L285_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.43 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H42 zenon_Ha3 zenon_Ha2 zenon_H9e zenon_H65 zenon_H50 zenon_H66 zenon_H95 zenon_H49 zenon_H3d zenon_H19. % 51.19/51.43 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.43 apply (zenon_L15_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.43 apply (zenon_L17_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.43 apply (zenon_L32_); trivial. % 51.19/51.43 apply (zenon_L37_); trivial. % 51.19/51.43 (* end of lemma zenon_L285_ *) % 51.19/51.43 assert (zenon_L286_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.43 do 0 intro. intros zenon_Hcf zenon_H49 zenon_H95 zenon_H50 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.19/51.43 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.43 apply (zenon_L285_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.43 apply (zenon_L40_); trivial. % 51.19/51.43 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.43 apply (zenon_L43_); trivial. % 51.19/51.43 apply (zenon_L37_); trivial. % 51.19/51.43 (* end of lemma zenon_L286_ *) % 51.19/51.43 assert (zenon_L287_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.19/51.43 do 0 intro. intros zenon_Hde zenon_H19 zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hbe zenon_H42 zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H50 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.19/51.44 apply (zenon_L286_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.19/51.44 apply (zenon_L34_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.19/51.44 apply (zenon_L45_); trivial. % 51.19/51.44 apply (zenon_L46_); trivial. % 51.19/51.44 (* end of lemma zenon_L287_ *) % 51.19/51.44 assert (zenon_L288_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H95 zenon_H50 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_H42 zenon_Ha3 zenon_Hcb zenon_H3d zenon_Hde zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.44 apply (zenon_L39_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.44 apply (zenon_L287_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L41_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L288_ *) % 51.19/51.44 assert (zenon_L289_ : ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2c8 zenon_H11a zenon_H2c9 zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19 zenon_H51. % 51.19/51.44 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.44 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 51.19/51.44 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 51.19/51.44 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 51.19/51.44 cut (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e12)) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2c9. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H85. % 51.19/51.44 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 51.19/51.44 cut (((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 51.19/51.44 congruence. % 51.19/51.44 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H7a | zenon_intro zenon_H7b ]. % 51.19/51.44 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (op1 (e11) (e11)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2cb. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H7a. % 51.19/51.44 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 51.19/51.44 cut (((op1 (e11) (e11)) = (op1 (op1 (e10) (e12)) (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 51.19/51.44 congruence. % 51.19/51.44 cut (((e11) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 51.19/51.44 cut (((e11) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 51.19/51.44 congruence. % 51.19/51.44 apply zenon_H2cd. apply sym_equal. exact zenon_H11a. % 51.19/51.44 apply zenon_H2cd. apply sym_equal. exact zenon_H11a. % 51.19/51.44 apply zenon_H7b. apply refl_equal. % 51.19/51.44 apply zenon_H7b. apply refl_equal. % 51.19/51.44 apply zenon_H2ca. apply sym_equal. exact zenon_H2c8. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.44 apply (zenon_L18_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.44 apply (zenon_L20_); trivial. % 51.19/51.44 apply (zenon_L22_); trivial. % 51.19/51.44 (* end of lemma zenon_L289_ *) % 51.19/51.44 assert (zenon_L290_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H72 zenon_H62 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.44 apply (zenon_L15_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.44 apply (zenon_L289_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.44 apply (zenon_L36_); trivial. % 51.19/51.44 apply (zenon_L37_); trivial. % 51.19/51.44 (* end of lemma zenon_L290_ *) % 51.19/51.44 assert (zenon_L291_ : (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2ce zenon_He6 zenon_H49 zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19 zenon_H51. % 51.19/51.44 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.19/51.44 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 51.19/51.44 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 51.19/51.44 apply (zenon_and_s _ _ zenon_H82). zenon_intro zenon_H85. zenon_intro zenon_H84. % 51.19/51.44 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.19/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2ce. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H99. % 51.19/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.19/51.44 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 51.19/51.44 congruence. % 51.19/51.44 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e13)) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2cf. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H84. % 51.19/51.44 cut (((e13) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2d0]. % 51.19/51.44 cut (((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 51.19/51.44 congruence. % 51.19/51.44 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.19/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (op1 (e12) (e12)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H98. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H99. % 51.19/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.19/51.44 cut (((op1 (e12) (e12)) = (op1 (op1 (e10) (e13)) (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 51.19/51.44 congruence. % 51.19/51.44 apply (zenon_L26_); trivial. % 51.19/51.44 apply zenon_H9a. apply refl_equal. % 51.19/51.44 apply zenon_H9a. apply refl_equal. % 51.19/51.44 apply zenon_H2d0. apply sym_equal. exact zenon_He6. % 51.19/51.44 apply zenon_H9a. apply refl_equal. % 51.19/51.44 apply zenon_H9a. apply refl_equal. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.19/51.44 apply (zenon_L18_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.19/51.44 apply (zenon_L20_); trivial. % 51.19/51.44 apply (zenon_L22_); trivial. % 51.19/51.44 (* end of lemma zenon_L291_ *) % 51.19/51.44 assert (zenon_L292_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H72 zenon_H62 zenon_He6 zenon_H2ce zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.19/51.44 apply (zenon_L15_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.19/51.44 apply (zenon_L291_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.19/51.44 apply (zenon_L36_); trivial. % 51.19/51.44 apply (zenon_L37_); trivial. % 51.19/51.44 (* end of lemma zenon_L292_ *) % 51.19/51.44 assert (zenon_L293_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H2ce zenon_He6 zenon_H62 zenon_H72 zenon_H4b zenon_Hb5 zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.44 apply (zenon_L292_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.44 apply (zenon_L40_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.44 apply (zenon_L43_); trivial. % 51.19/51.44 apply (zenon_L37_); trivial. % 51.19/51.44 (* end of lemma zenon_L293_ *) % 51.19/51.44 assert (zenon_L294_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H90 zenon_H35 zenon_Hda zenon_Hd3 zenon_Hde zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hbe zenon_H42 zenon_Hb5 zenon_H4b zenon_H72 zenon_He6 zenon_H2ce zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.44 apply (zenon_L47_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.44 apply (zenon_L287_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L293_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L294_ *) % 51.19/51.44 assert (zenon_L295_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H2ce zenon_He6 zenon_H72 zenon_H4b zenon_Hb5 zenon_H42 zenon_Ha3 zenon_Hcb zenon_H3d zenon_Hde zenon_Hd3 zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.44 apply (zenon_L39_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.44 apply (zenon_L294_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L41_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L295_ *) % 51.19/51.44 assert (zenon_L296_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2d1 zenon_H126 zenon_H125 zenon_H66 zenon_H2c8 zenon_H2c9 zenon_H62 zenon_H2be zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H2ce zenon_H72 zenon_H4b zenon_Hb5 zenon_H42 zenon_Ha3 zenon_Hcb zenon_H3d zenon_Hde zenon_Hd3 zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H22 | zenon_intro zenon_H2d2 ]. % 51.19/51.44 apply (zenon_L100_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H11a | zenon_intro zenon_H2d3 ]. % 51.19/51.44 apply (zenon_L290_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H2bf | zenon_intro zenon_He6 ]. % 51.19/51.44 apply (zenon_L282_); trivial. % 51.19/51.44 apply (zenon_L295_); trivial. % 51.19/51.44 (* end of lemma zenon_L296_ *) % 51.19/51.44 assert (zenon_L297_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H90 zenon_H35 zenon_Hda zenon_Hd3 zenon_Hde zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H2be zenon_H62 zenon_H2c9 zenon_H2c8 zenon_H125 zenon_H126 zenon_H2d1 zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.44 apply (zenon_L296_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.44 apply (zenon_L42_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.44 apply (zenon_L43_); trivial. % 51.19/51.44 apply (zenon_L37_); trivial. % 51.19/51.44 (* end of lemma zenon_L297_ *) % 51.19/51.44 assert (zenon_L298_ : (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H1c zenon_H2d1 zenon_H126 zenon_H125 zenon_H2c8 zenon_H2c9 zenon_H2be zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H2ce zenon_H72 zenon_H4b zenon_Hb5 zenon_Hde zenon_Hd3 zenon_Hda zenon_H35 zenon_H90 zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.44 apply (zenon_L16_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.44 apply (zenon_L288_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L297_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L298_ *) % 51.19/51.44 assert (zenon_L299_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2d4 zenon_H19 zenon_H1b zenon_H105 zenon_H3b zenon_H1c zenon_H2c zenon_H2ba zenon_H45 zenon_H47. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d | zenon_intro zenon_H2d5 ]. % 51.19/51.44 apply (zenon_L4_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H104 | zenon_intro zenon_H2d6 ]. % 51.19/51.44 apply (zenon_L73_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H2bb | zenon_intro zenon_H46 ]. % 51.19/51.44 apply (zenon_L281_); trivial. % 51.19/51.44 apply (zenon_L13_); trivial. % 51.19/51.44 (* end of lemma zenon_L299_ *) % 51.19/51.44 assert (zenon_L300_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hf8 zenon_H34 zenon_H45 zenon_H2ba zenon_H2c zenon_H1c zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H19 zenon_H3d zenon_Hcb zenon_Hbe zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_Hcf zenon_H50 zenon_H42. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.44 apply (zenon_L86_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.44 apply (zenon_L299_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.44 apply (zenon_L286_); trivial. % 51.19/51.44 apply (zenon_L17_); trivial. % 51.19/51.44 (* end of lemma zenon_L300_ *) % 51.19/51.44 assert (zenon_L301_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H90 zenon_H35 zenon_H49 zenon_H42 zenon_H51 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.44 apply (zenon_L16_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.44 apply (zenon_L17_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L289_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L301_ *) % 51.19/51.44 assert (zenon_L302_ : (~((op1 (e13) (op1 (e13) (e13))) = (op1 (e11) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e12)) = (e10)) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2d7 zenon_Hbe zenon_H19 zenon_H126. % 51.19/51.44 cut (((op1 (e13) (e11)) = (e10)) = ((op1 (e13) (op1 (e13) (e13))) = (op1 (e11) (e12)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2d7. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_Hbe. % 51.19/51.44 cut (((e10) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 51.19/51.44 cut (((op1 (e13) (e11)) = (op1 (e13) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 51.19/51.44 congruence. % 51.19/51.44 elim (classic ((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13))))); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H2da ]. % 51.19/51.44 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e13) (e11)) = (op1 (e13) (op1 (e13) (e13))))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2d8. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H2d9. % 51.19/51.44 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 51.19/51.44 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 51.19/51.44 congruence. % 51.19/51.44 apply (zenon_L3_); trivial. % 51.19/51.44 apply zenon_H2da. apply refl_equal. % 51.19/51.44 apply zenon_H2da. apply refl_equal. % 51.19/51.44 apply zenon_H127. apply sym_equal. exact zenon_H126. % 51.19/51.44 (* end of lemma zenon_L302_ *) % 51.19/51.44 assert (zenon_L303_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H1c zenon_H50 zenon_Hbe zenon_H126 zenon_H19 zenon_H2db. % 51.19/51.44 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 51.19/51.44 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e11) (e12)) = (op1 (e11) (e13)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2db. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_Ha7. % 51.19/51.44 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 51.19/51.44 cut (((op1 (e11) (e13)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2dc]. % 51.19/51.44 congruence. % 51.19/51.44 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e11) (e13)) = (op1 (e11) (e12)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H2dc. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H1c. % 51.19/51.44 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 51.19/51.44 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 51.19/51.44 congruence. % 51.19/51.44 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_Ha7 | zenon_intro zenon_Ha8 ]. % 51.19/51.44 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e10) = (op1 (e11) (e13)))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H9c. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_Ha7. % 51.19/51.44 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 51.19/51.44 cut (((op1 (e11) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2dd]. % 51.19/51.44 congruence. % 51.19/51.44 exact (zenon_H2dd zenon_H50). % 51.19/51.44 apply zenon_Ha8. apply refl_equal. % 51.19/51.44 apply zenon_Ha8. apply refl_equal. % 51.19/51.44 apply (zenon_L302_); trivial. % 51.19/51.44 apply zenon_Ha8. apply refl_equal. % 51.19/51.44 apply zenon_Ha8. apply refl_equal. % 51.19/51.44 (* end of lemma zenon_L303_ *) % 51.19/51.44 assert (zenon_L304_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hb0 zenon_H2db zenon_H126 zenon_Hbe zenon_Hab zenon_H1c zenon_H2c zenon_H2ce zenon_He6 zenon_H49 zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.19/51.44 apply (zenon_L303_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.19/51.44 apply (zenon_L33_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.19/51.44 apply (zenon_L34_); trivial. % 51.19/51.44 apply (zenon_L291_); trivial. % 51.19/51.44 (* end of lemma zenon_L304_ *) % 51.19/51.44 assert (zenon_L305_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e10) = (e11))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2d1 zenon_H24 zenon_H23 zenon_H8c zenon_H2c8 zenon_H2c9 zenon_H51 zenon_H42 zenon_H35 zenon_H90 zenon_H2be zenon_Hb0 zenon_H2db zenon_H126 zenon_Hbe zenon_Hab zenon_H1c zenon_H2c zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H22 | zenon_intro zenon_H2d2 ]. % 51.19/51.44 apply (zenon_L5_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H11a | zenon_intro zenon_H2d3 ]. % 51.19/51.44 apply (zenon_L301_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H2bf | zenon_intro zenon_He6 ]. % 51.19/51.44 apply (zenon_L282_); trivial. % 51.19/51.44 apply (zenon_L304_); trivial. % 51.19/51.44 (* end of lemma zenon_L305_ *) % 51.19/51.44 assert (zenon_L306_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hcf zenon_H72 zenon_H65 zenon_H2ce zenon_H2c zenon_Hab zenon_Hbe zenon_H126 zenon_H2db zenon_Hb0 zenon_H2be zenon_H90 zenon_H35 zenon_H2c9 zenon_H2c8 zenon_H23 zenon_H24 zenon_H2d1 zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hda zenon_H49 zenon_H7d zenon_H62 zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_H19. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.19/51.44 apply (zenon_L305_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.19/51.44 apply (zenon_L42_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.19/51.44 apply (zenon_L51_); trivial. % 51.19/51.44 apply (zenon_L37_); trivial. % 51.19/51.44 (* end of lemma zenon_L306_ *) % 51.19/51.44 assert (zenon_L307_ : (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (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) (e10)) = (e10)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hd3 zenon_Hde zenon_H95 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_Hcb zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_H34 zenon_Hf8 zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H1c zenon_H2d1 zenon_H24 zenon_H23 zenon_H2c8 zenon_H2c9 zenon_H35 zenon_H90 zenon_H2be zenon_Hb0 zenon_H2db zenon_H126 zenon_Hbe zenon_Hab zenon_H2c zenon_H2ce zenon_H65 zenon_H72 zenon_Hcf zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.44 apply (zenon_L47_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.44 apply (zenon_L300_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L306_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L307_ *) % 51.19/51.44 assert (zenon_L308_ : ((op1 (e13) (e11)) = (e10)) -> ((op1 (e13) (e11)) = (e12)) -> (~((e10) = (e12))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hbe zenon_H2de zenon_H35. % 51.19/51.44 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.19/51.44 cut (((e12) = (e12)) = ((e10) = (e12))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H35. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_H36. % 51.19/51.44 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.19/51.44 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 51.19/51.44 congruence. % 51.19/51.44 cut (((op1 (e13) (e11)) = (e10)) = ((e12) = (e10))). % 51.19/51.44 intro zenon_D_pnotp. % 51.19/51.44 apply zenon_H38. % 51.19/51.44 rewrite <- zenon_D_pnotp. % 51.19/51.44 exact zenon_Hbe. % 51.19/51.44 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.19/51.44 cut (((op1 (e13) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2df]. % 51.19/51.44 congruence. % 51.19/51.44 exact (zenon_H2df zenon_H2de). % 51.19/51.44 apply zenon_H32. apply refl_equal. % 51.19/51.44 apply zenon_H37. apply refl_equal. % 51.19/51.44 apply zenon_H37. apply refl_equal. % 51.19/51.44 (* end of lemma zenon_L308_ *) % 51.19/51.44 assert (zenon_L309_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H35 zenon_H2de zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.44 apply (zenon_L39_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.44 apply (zenon_L308_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L41_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L309_ *) % 51.19/51.44 assert (zenon_L310_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e10)) = (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)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2e0 zenon_H10e zenon_H35 zenon_Haf zenon_H125 zenon_H72 zenon_H2ce zenon_H2db zenon_Hb0 zenon_H2be zenon_H90 zenon_H2c9 zenon_H23 zenon_H24 zenon_H2d1 zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H2c5 zenon_H2e1 zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H42. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.19/51.44 apply (zenon_L9_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.19/51.44 apply (zenon_L283_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.19/51.44 apply (zenon_L281_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.19/51.44 apply (zenon_L284_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.44 apply (zenon_L86_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.44 apply (zenon_L13_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.44 apply (zenon_L298_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.44 apply (zenon_L39_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.44 apply (zenon_L307_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L41_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 apply (zenon_L309_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.44 apply (zenon_L86_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.44 apply (zenon_L13_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.44 apply (zenon_L288_); trivial. % 51.19/51.44 apply (zenon_L17_); trivial. % 51.19/51.44 (* end of lemma zenon_L310_ *) % 51.19/51.44 assert (zenon_L311_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H1c zenon_Hc2 zenon_H90 zenon_H35 zenon_Hda zenon_Hd3 zenon_Hde zenon_H3d zenon_Hcb zenon_Ha3 zenon_H42 zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H2be zenon_H2c9 zenon_H2c8 zenon_H66 zenon_H125 zenon_H126 zenon_H2d1 zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.44 apply (zenon_L47_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.44 apply (zenon_L285_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L296_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L311_ *) % 51.19/51.44 assert (zenon_L312_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_H2ce zenon_H2c zenon_H1c zenon_Hab zenon_Hbe zenon_H126 zenon_H2db zenon_Hb0 zenon_H2be zenon_H90 zenon_H35 zenon_H42 zenon_H51 zenon_H2c9 zenon_H2c8 zenon_H23 zenon_H24 zenon_H2d1 zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.19/51.44 apply (zenon_L16_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.19/51.44 apply (zenon_L17_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L305_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 (* end of lemma zenon_L312_ *) % 51.19/51.44 assert (zenon_L313_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e10)) = (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 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_H2ce zenon_H2c zenon_Hab zenon_H126 zenon_H2db zenon_Hb0 zenon_H2be zenon_H90 zenon_H42 zenon_H2c9 zenon_H23 zenon_H24 zenon_H2d1 zenon_Hda zenon_Hd3 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Haf zenon_H95 zenon_H9e zenon_Ha2 zenon_Hcf zenon_H125 zenon_H45 zenon_H46 zenon_H34 zenon_Hf8 zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.19/51.44 apply (zenon_L281_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.19/51.44 apply (zenon_L284_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.44 apply (zenon_L86_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.44 apply (zenon_L13_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.44 apply (zenon_L311_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.19/51.44 apply (zenon_L39_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.19/51.44 apply (zenon_L312_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.19/51.44 apply (zenon_L41_); trivial. % 51.19/51.44 apply (zenon_L24_); trivial. % 51.19/51.44 apply (zenon_L309_); trivial. % 51.19/51.44 (* end of lemma zenon_L313_ *) % 51.19/51.44 assert (zenon_L314_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_H19 zenon_H3d zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_H50 zenon_H42. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.19/51.44 apply (zenon_L86_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.19/51.44 apply (zenon_L13_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.19/51.44 apply (zenon_L285_); trivial. % 51.19/51.44 apply (zenon_L17_); trivial. % 51.19/51.44 (* end of lemma zenon_L314_ *) % 51.19/51.44 assert (zenon_L315_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (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) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H2e0 zenon_H10e zenon_H8c zenon_H1c zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H125 zenon_Hcf zenon_Haf zenon_Hcb zenon_Hde zenon_Hd3 zenon_Hda zenon_H2d1 zenon_H24 zenon_H23 zenon_H2c9 zenon_H90 zenon_H2be zenon_Hb0 zenon_H2db zenon_Hab zenon_H2c zenon_H2ce zenon_H54 zenon_H72 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_H19 zenon_H3d zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_H42. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.19/51.44 apply (zenon_L9_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.19/51.44 apply (zenon_L283_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.19/51.44 apply (zenon_L313_); trivial. % 51.19/51.44 apply (zenon_L314_); trivial. % 51.19/51.44 (* end of lemma zenon_L315_ *) % 51.19/51.44 assert (zenon_L316_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (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) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_Hfb zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_He1 zenon_H7d zenon_H2e0 zenon_H10e zenon_H8c zenon_H1c zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H125 zenon_Hcf zenon_Haf zenon_Hcb zenon_Hde zenon_Hd3 zenon_Hda zenon_H2d1 zenon_H24 zenon_H23 zenon_H2c9 zenon_H90 zenon_H2be zenon_Hb0 zenon_H2db zenon_Hab zenon_H2c zenon_H2ce zenon_H54 zenon_H72 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_H19 zenon_H3d zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_H42. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.19/51.44 apply (zenon_L11_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.19/51.44 apply (zenon_L86_); trivial. % 51.19/51.44 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.19/51.44 apply (zenon_L310_); trivial. % 51.19/51.44 apply (zenon_L315_); trivial. % 51.19/51.44 (* end of lemma zenon_L316_ *) % 51.19/51.44 assert (zenon_L317_ : ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e10)) = (e13)) -> (~((e10) = (e13))) -> False). % 51.19/51.44 do 0 intro. intros zenon_H23 zenon_H3c zenon_H42. % 51.19/51.44 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.27/51.44 cut (((e13) = (e13)) = ((e10) = (e13))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H42. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H3e. % 51.27/51.44 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.27/51.44 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((op1 (e10) (e10)) = (e10)) = ((e13) = (e10))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H43. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H23. % 51.27/51.44 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.27/51.44 cut (((op1 (e10) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 51.27/51.44 congruence. % 51.27/51.44 exact (zenon_H40 zenon_H3c). % 51.27/51.44 apply zenon_H32. apply refl_equal. % 51.27/51.44 apply zenon_H17. apply refl_equal. % 51.27/51.44 apply zenon_H17. apply refl_equal. % 51.27/51.44 (* end of lemma zenon_L317_ *) % 51.27/51.44 assert (zenon_L318_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hcf zenon_H72 zenon_H65 zenon_He6 zenon_H2ce zenon_H42 zenon_Hbe zenon_Hda zenon_H49 zenon_H7d zenon_H62 zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_H19. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.27/51.44 apply (zenon_L291_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.27/51.44 apply (zenon_L40_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.27/51.44 apply (zenon_L51_); trivial. % 51.27/51.44 apply (zenon_L37_); trivial. % 51.27/51.44 (* end of lemma zenon_L318_ *) % 51.27/51.44 assert (zenon_L319_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H90 zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_Hbe zenon_H42 zenon_H2ce zenon_He6 zenon_H65 zenon_H72 zenon_Hcf zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.44 apply (zenon_L47_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.44 apply (zenon_L17_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L318_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L319_ *) % 51.27/51.44 assert (zenon_L320_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H72 zenon_H65 zenon_He6 zenon_H2ce zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.27/51.44 apply (zenon_L39_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.27/51.44 apply (zenon_L319_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L41_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L320_ *) % 51.27/51.44 assert (zenon_L321_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H90 zenon_H35 zenon_H42 zenon_H51 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_He6 zenon_H2ce zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.44 apply (zenon_L16_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.44 apply (zenon_L17_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L291_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L321_ *) % 51.27/51.44 assert (zenon_L322_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hf8 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hb5 zenon_H4b zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H3d zenon_Hf6 zenon_H33 zenon_H90 zenon_H35 zenon_H42 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_He6 zenon_H2ce zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.27/51.44 apply (zenon_L12_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.27/51.44 apply (zenon_L299_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.44 apply (zenon_L16_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.44 apply (zenon_L66_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L292_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 apply (zenon_L321_); trivial. % 51.27/51.44 (* end of lemma zenon_L322_ *) % 51.27/51.44 assert (zenon_L323_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H90 zenon_Hda zenon_Hd3 zenon_H35 zenon_Hde zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_He6 zenon_H2ce zenon_H2c zenon_H1c zenon_Hab zenon_Hbe zenon_H126 zenon_H2db zenon_Hb0 zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.44 apply (zenon_L47_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.44 apply (zenon_L303_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L304_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L323_ *) % 51.27/51.44 assert (zenon_L324_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hb0 zenon_H2db zenon_H126 zenon_Hab zenon_H2c zenon_H2ce zenon_He6 zenon_H49 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_Hde zenon_H35 zenon_Hd3 zenon_Hda zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.27/51.44 apply (zenon_L39_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.27/51.44 apply (zenon_L323_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L41_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L324_ *) % 51.27/51.44 assert (zenon_L325_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hff zenon_H2e1 zenon_H2c5 zenon_H2be zenon_H2c9 zenon_H24 zenon_H2d1 zenon_H125 zenon_H8c zenon_H19 zenon_H2ce zenon_H54 zenon_H65 zenon_H72 zenon_H42 zenon_H35 zenon_H90 zenon_Hb5 zenon_Ha2 zenon_H9e zenon_H95 zenon_H3d zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H1c zenon_H2c zenon_H2ba zenon_H45 zenon_H34 zenon_Hf8 zenon_Hc8 zenon_Hb8 zenon_Hb0 zenon_H2db zenon_Hab zenon_Hde zenon_Hd3 zenon_Hda zenon_Hc2 zenon_H10e zenon_Haf zenon_Hf6 zenon_H2e0 zenon_Hcb zenon_Hcf zenon_H7d zenon_He1 zenon_H23 zenon_Hfb zenon_H49 zenon_H4b. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.27/51.44 apply (zenon_L11_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.27/51.44 apply (zenon_L316_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.27/51.44 apply (zenon_L317_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.27/51.44 apply (zenon_L86_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.27/51.44 apply (zenon_L86_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.27/51.44 apply (zenon_L299_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.27/51.44 apply (zenon_L295_); trivial. % 51.27/51.44 apply (zenon_L320_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.27/51.44 apply (zenon_L322_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.27/51.44 apply (zenon_L283_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.27/51.44 apply (zenon_L324_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.27/51.44 apply (zenon_L86_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.27/51.44 apply (zenon_L299_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.27/51.44 apply (zenon_L285_); trivial. % 51.27/51.44 apply (zenon_L321_); trivial. % 51.27/51.44 apply (zenon_L15_); trivial. % 51.27/51.44 (* end of lemma zenon_L325_ *) % 51.27/51.44 assert (zenon_L326_ : (~((h4 (e11)) = (e21))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2e6 zenon_H2e7 zenon_H14e. % 51.27/51.44 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (e11)) = (e21))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2e6. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2e7. % 51.27/51.44 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 51.27/51.44 cut (((h4 (e11)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2e8]. % 51.27/51.44 congruence. % 51.27/51.44 apply zenon_H2e8. apply refl_equal. % 51.27/51.44 apply zenon_H14f. apply sym_equal. exact zenon_H14e. % 51.27/51.44 (* end of lemma zenon_L326_ *) % 51.27/51.44 assert (zenon_L327_ : (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((op1 (e10) (e11)) = (e13)) -> ((op2 (e20) (e21)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2e9 zenon_H2ea zenon_H46 zenon_H244 zenon_H13 zenon_H14 zenon_H2e7 zenon_H14e. % 51.27/51.44 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2e9. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2ea. % 51.27/51.44 cut (((e23) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2eb]. % 51.27/51.44 cut (((h4 (e13)) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [ zenon_intro zenon_H2ed | zenon_intro zenon_H2ee ]. % 51.27/51.44 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11)))) = ((h4 (e13)) = (h4 (op1 (e10) (e11))))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2ec. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2ed. % 51.27/51.44 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2ee]. % 51.27/51.44 cut (((h4 (op1 (e10) (e11))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2ef]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((op1 (e10) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f0]. % 51.27/51.44 congruence. % 51.27/51.44 exact (zenon_H2f0 zenon_H46). % 51.27/51.44 apply zenon_H2ee. apply refl_equal. % 51.27/51.44 apply zenon_H2ee. apply refl_equal. % 51.27/51.44 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H2f1 | zenon_intro zenon_H2f2 ]. % 51.27/51.44 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((e23) = (op2 (h4 (e10)) (h4 (e11))))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2eb. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2f1. % 51.27/51.44 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2f2]. % 51.27/51.44 cut (((op2 (h4 (e10)) (h4 (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2f3]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((op2 (e20) (e21)) = (e23)) = ((op2 (h4 (e10)) (h4 (e11))) = (e23))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2f3. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H244. % 51.27/51.44 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.27/51.44 cut (((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2f4]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H2f1 | zenon_intro zenon_H2f2 ]. % 51.27/51.44 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2f4. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2f1. % 51.27/51.44 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2f2]. % 51.27/51.44 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2f5]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 51.27/51.44 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 51.27/51.44 congruence. % 51.27/51.44 apply (zenon_L1_); trivial. % 51.27/51.44 apply (zenon_L326_); trivial. % 51.27/51.44 apply zenon_H2f2. apply refl_equal. % 51.27/51.44 apply zenon_H2f2. apply refl_equal. % 51.27/51.44 apply zenon_H14c. apply refl_equal. % 51.27/51.44 apply zenon_H2f2. apply refl_equal. % 51.27/51.44 apply zenon_H2f2. apply refl_equal. % 51.27/51.44 (* end of lemma zenon_L327_ *) % 51.27/51.44 assert (zenon_L328_ : ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e11) = (e13))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H108 zenon_H41 zenon_H3d. % 51.27/51.44 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.27/51.44 cut (((e13) = (e13)) = ((e11) = (e13))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H3d. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H3e. % 51.27/51.44 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.27/51.44 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((op1 (e11) (e10)) = (e11)) = ((e13) = (e11))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H3f. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H108. % 51.27/51.44 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.27/51.44 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 51.27/51.44 congruence. % 51.27/51.44 exact (zenon_H44 zenon_H41). % 51.27/51.44 apply zenon_H3a. apply refl_equal. % 51.27/51.44 apply zenon_H17. apply refl_equal. % 51.27/51.44 apply zenon_H17. apply refl_equal. % 51.27/51.44 (* end of lemma zenon_L328_ *) % 51.27/51.44 assert (zenon_L329_ : (~((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2f6 zenon_H49 zenon_H1c zenon_H7c. % 51.27/51.44 cut (((op1 (e10) (e13)) = (e12)) = ((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e12) (e10)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2f6. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H49. % 51.27/51.44 cut (((e12) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 51.27/51.44 cut (((op1 (e10) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2f7]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [ zenon_intro zenon_H2f8 | zenon_intro zenon_H2f9 ]. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e10) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2f7. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2f8. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2f9]. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 51.27/51.44 congruence. % 51.27/51.44 apply (zenon_L6_); trivial. % 51.27/51.44 apply zenon_H2f9. apply refl_equal. % 51.27/51.44 apply zenon_H2f9. apply refl_equal. % 51.27/51.44 apply zenon_H86. apply sym_equal. exact zenon_H7c. % 51.27/51.44 (* end of lemma zenon_L329_ *) % 51.27/51.44 assert (zenon_L330_ : (~((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2fa zenon_H1c zenon_H7c zenon_H49 zenon_H2c6. % 51.27/51.44 cut (((op1 (e12) (e10)) = (e12)) = ((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e11)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2fa. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H7c. % 51.27/51.44 cut (((e12) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 51.27/51.44 cut (((op1 (e12) (e10)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2fb]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [ zenon_intro zenon_H2f8 | zenon_intro zenon_H2f9 ]. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e12) (e10)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2fb. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2f8. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2f9]. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 51.27/51.44 congruence. % 51.27/51.44 apply (zenon_L329_); trivial. % 51.27/51.44 apply zenon_H2f9. apply refl_equal. % 51.27/51.44 apply zenon_H2f9. apply refl_equal. % 51.27/51.44 apply zenon_H2c7. apply sym_equal. exact zenon_H2c6. % 51.27/51.44 (* end of lemma zenon_L330_ *) % 51.27/51.44 assert (zenon_L331_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e11) (e12)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2c zenon_H12b zenon_H2c6 zenon_H1c zenon_H7c zenon_H49 zenon_Ha2. % 51.27/51.44 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H2fc | zenon_intro zenon_Hce ]. % 51.27/51.44 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e11) (e11)) = (op1 (e11) (e12)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_Ha2. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2fc. % 51.27/51.44 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 51.27/51.44 cut (((op1 (e11) (e12)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2fd]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e11) (e12)) = (op1 (e11) (e11)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2fd. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2c. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 51.27/51.44 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H2fc | zenon_intro zenon_Hce ]. % 51.27/51.44 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e12) = (op1 (e11) (e12)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H12e. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2fc. % 51.27/51.44 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hce]. % 51.27/51.44 cut (((op1 (e11) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2fe]. % 51.27/51.44 congruence. % 51.27/51.44 exact (zenon_H2fe zenon_H12b). % 51.27/51.44 apply zenon_Hce. apply refl_equal. % 51.27/51.44 apply zenon_Hce. apply refl_equal. % 51.27/51.44 apply (zenon_L330_); trivial. % 51.27/51.44 apply zenon_Hce. apply refl_equal. % 51.27/51.44 apply zenon_Hce. apply refl_equal. % 51.27/51.44 (* end of lemma zenon_L331_ *) % 51.27/51.44 assert (zenon_L332_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2c zenon_H2c8 zenon_H49 zenon_H7c zenon_H1c zenon_H2ff. % 51.27/51.44 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H300 | zenon_intro zenon_H301 ]. % 51.27/51.44 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e12) (e10)) = (op1 (e12) (e11)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2ff. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H300. % 51.27/51.44 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H301]. % 51.27/51.44 cut (((op1 (e12) (e11)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H302]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e12) (e11)) = (op1 (e12) (e10)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H302. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2c. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 51.27/51.44 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H300 | zenon_intro zenon_H301 ]. % 51.27/51.44 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e12) = (op1 (e12) (e11)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H2ca. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H300. % 51.27/51.44 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H301]. % 51.27/51.44 cut (((op1 (e12) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H303]. % 51.27/51.44 congruence. % 51.27/51.44 exact (zenon_H303 zenon_H2c8). % 51.27/51.44 apply zenon_H301. apply refl_equal. % 51.27/51.44 apply zenon_H301. apply refl_equal. % 51.27/51.44 apply (zenon_L329_); trivial. % 51.27/51.44 apply zenon_H301. apply refl_equal. % 51.27/51.44 apply zenon_H301. apply refl_equal. % 51.27/51.44 (* end of lemma zenon_L332_ *) % 51.27/51.44 assert (zenon_L333_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2e1 zenon_H2ba zenon_Ha2 zenon_H12b zenon_H2ff zenon_H7c zenon_H49 zenon_H2c zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.27/51.44 apply (zenon_L281_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.27/51.44 apply (zenon_L331_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.27/51.44 apply (zenon_L332_); trivial. % 51.27/51.44 apply (zenon_L309_); trivial. % 51.27/51.44 (* end of lemma zenon_L333_ *) % 51.27/51.44 assert (zenon_L334_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2c zenon_H304 zenon_H49 zenon_H7c zenon_H1c zenon_H305. % 51.27/51.44 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e12) (e10)) = (op1 (e12) (e12)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H305. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H99. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H306]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e12) (e12)) = (op1 (e12) (e10)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H306. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2c. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 51.27/51.44 cut (((e12) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e12) = (op1 (e12) (e12)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H307. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H99. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.27/51.44 cut (((op1 (e12) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 51.27/51.44 congruence. % 51.27/51.44 exact (zenon_H308 zenon_H304). % 51.27/51.44 apply zenon_H9a. apply refl_equal. % 51.27/51.44 apply zenon_H9a. apply refl_equal. % 51.27/51.44 apply (zenon_L329_); trivial. % 51.27/51.44 apply zenon_H9a. apply refl_equal. % 51.27/51.44 apply zenon_H9a. apply refl_equal. % 51.27/51.44 (* end of lemma zenon_L334_ *) % 51.27/51.44 assert (zenon_L335_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hde zenon_H4b zenon_H4a zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.27/51.44 apply (zenon_L15_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.27/51.44 apply (zenon_L34_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.27/51.44 apply (zenon_L45_); trivial. % 51.27/51.44 apply (zenon_L46_); trivial. % 51.27/51.44 (* end of lemma zenon_L335_ *) % 51.27/51.44 assert (zenon_L336_ : (((op1 (op1 (e13) (e10)) (op1 (e13) (e10))) = (e10))/\(((op1 (op1 (e13) (e11)) (op1 (e13) (e11))) = (e11))/\(((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e12))/\((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> False). % 51.27/51.44 do 0 intro. intros zenon_H71 zenon_He1 zenon_Hf1. % 51.27/51.44 apply (zenon_and_s _ _ zenon_H71). zenon_intro zenon_H74. zenon_intro zenon_H73. % 51.27/51.44 apply (zenon_and_s _ _ zenon_H73). zenon_intro zenon_H76. zenon_intro zenon_H75. % 51.27/51.44 apply (zenon_and_s _ _ zenon_H75). zenon_intro zenon_H78. zenon_intro zenon_H77. % 51.27/51.44 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (e12)) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_He1. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H78. % 51.27/51.44 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 51.27/51.44 cut (((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H309]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (op1 (e13) (e12)) (op1 (e13) (e12))) = (op1 (e12) (e12)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H309. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H99. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.27/51.44 cut (((op1 (e12) (e12)) = (op1 (op1 (e13) (e12)) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H30a]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 51.27/51.44 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 51.27/51.44 congruence. % 51.27/51.44 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 51.27/51.44 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 51.27/51.44 apply zenon_H9a. apply refl_equal. % 51.27/51.44 apply zenon_H9a. apply refl_equal. % 51.27/51.44 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 51.27/51.44 (* end of lemma zenon_L336_ *) % 51.27/51.44 assert (zenon_L337_ : ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (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) (e12)) = (e12)) -> False). % 51.27/51.44 do 0 intro. intros zenon_H49 zenon_H95 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_H96 zenon_He1 zenon_Hf1. % 51.27/51.44 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.27/51.44 apply (zenon_L27_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.27/51.44 apply (zenon_L58_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.27/51.44 apply (zenon_L30_); trivial. % 51.27/51.44 apply (zenon_L336_); trivial. % 51.27/51.44 (* end of lemma zenon_L337_ *) % 51.27/51.44 assert (zenon_L338_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hb5 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H4b zenon_Hde zenon_H42 zenon_Hf1 zenon_He1 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_H95 zenon_H49 zenon_H3d zenon_H19. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.27/51.44 apply (zenon_L335_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.27/51.44 apply (zenon_L17_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.27/51.44 apply (zenon_L337_); trivial. % 51.27/51.44 apply (zenon_L37_); trivial. % 51.27/51.44 (* end of lemma zenon_L338_ *) % 51.27/51.44 assert (zenon_L339_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H90 zenon_H35 zenon_H3d zenon_H95 zenon_H41 zenon_Hea zenon_H9e zenon_He1 zenon_Hf1 zenon_H42 zenon_Hde zenon_H4b zenon_Hd3 zenon_Hda zenon_Hb5 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_He6 zenon_H2ce zenon_H2c zenon_H1c zenon_Hab zenon_Hbe zenon_H126 zenon_H2db zenon_Hb0 zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.44 apply (zenon_L16_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.44 apply (zenon_L338_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L304_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L339_ *) % 51.27/51.44 assert (zenon_L340_ : (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> False). % 51.27/51.44 do 0 intro. intros zenon_H45 zenon_H104 zenon_H30b. % 51.27/51.44 cut (((op1 (e10) (e11)) = (e11)) = ((op1 (e10) (e11)) = (op1 (e11) (e11)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H45. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H104. % 51.27/51.44 cut (((e11) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 51.27/51.44 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 51.27/51.44 congruence. % 51.27/51.44 apply zenon_H20. apply refl_equal. % 51.27/51.44 apply zenon_H30c. apply sym_equal. exact zenon_H30b. % 51.27/51.44 (* end of lemma zenon_L340_ *) % 51.27/51.44 assert (zenon_L341_ : ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H2c zenon_He8 zenon_H49 zenon_H7c zenon_H1c zenon_H30d. % 51.27/51.44 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hbc ]. % 51.27/51.44 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e12) (e10)) = (op1 (e13) (e10)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H30d. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_Hbb. % 51.27/51.44 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 51.27/51.44 cut (((op1 (e13) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30e]. % 51.27/51.44 congruence. % 51.27/51.44 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e13) (e10)) = (op1 (e12) (e10)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H30e. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_H2c. % 51.27/51.44 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2f6]. % 51.27/51.44 cut (((e12) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H30f]. % 51.27/51.44 congruence. % 51.27/51.44 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_Hbb | zenon_intro zenon_Hbc ]. % 51.27/51.44 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e12) = (op1 (e13) (e10)))). % 51.27/51.44 intro zenon_D_pnotp. % 51.27/51.44 apply zenon_H30f. % 51.27/51.44 rewrite <- zenon_D_pnotp. % 51.27/51.44 exact zenon_Hbb. % 51.27/51.44 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 51.27/51.44 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H310]. % 51.27/51.44 congruence. % 51.27/51.44 exact (zenon_H310 zenon_He8). % 51.27/51.44 apply zenon_Hbc. apply refl_equal. % 51.27/51.44 apply zenon_Hbc. apply refl_equal. % 51.27/51.44 apply (zenon_L329_); trivial. % 51.27/51.44 apply zenon_Hbc. apply refl_equal. % 51.27/51.44 apply zenon_Hbc. apply refl_equal. % 51.27/51.44 (* end of lemma zenon_L341_ *) % 51.27/51.44 assert (zenon_L342_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H90 zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H3d zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hcc zenon_H49 zenon_Hda zenon_H42 zenon_H4b zenon_Hb5 zenon_H121 zenon_H123 zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.44 apply (zenon_L47_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.44 apply (zenon_L93_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L88_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L342_ *) % 51.27/51.44 assert (zenon_L343_ : (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e10)) = (e10)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H8c zenon_H19 zenon_H123 zenon_H121 zenon_Hb5 zenon_H4b zenon_H42 zenon_Hcc zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H3d zenon_Hde zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.27/51.44 apply (zenon_L342_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.27/51.44 apply (zenon_L34_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.27/51.44 apply (zenon_L45_); trivial. % 51.27/51.44 apply (zenon_L46_); trivial. % 51.27/51.44 (* end of lemma zenon_L343_ *) % 51.27/51.44 assert (zenon_L344_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H49 zenon_Hcc zenon_H10e zenon_H10a zenon_H51 zenon_H54 zenon_He1 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.27/51.44 apply (zenon_L39_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.27/51.44 apply (zenon_L77_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L41_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L344_ *) % 51.27/51.44 assert (zenon_L345_ : (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H95 zenon_H54 zenon_H51 zenon_H9e zenon_H96 zenon_Hcc zenon_H49 zenon_Hda. % 51.27/51.44 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.27/51.44 apply (zenon_L27_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.27/51.44 apply (zenon_L18_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.27/51.44 apply (zenon_L30_); trivial. % 51.27/51.44 apply (zenon_L50_); trivial. % 51.27/51.44 (* end of lemma zenon_L345_ *) % 51.27/51.44 assert (zenon_L346_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hb0 zenon_H3d zenon_He1 zenon_H41 zenon_Hea zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H8c zenon_He8 zenon_H4b zenon_Hcf zenon_H19 zenon_Hab zenon_H1c zenon_H2c zenon_H95 zenon_H54 zenon_H9e zenon_H96 zenon_Hcc zenon_H49 zenon_Hda. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.27/51.44 apply (zenon_L60_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.27/51.44 apply (zenon_L33_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.27/51.44 apply (zenon_L34_); trivial. % 51.27/51.44 apply (zenon_L345_); trivial. % 51.27/51.44 (* end of lemma zenon_L346_ *) % 51.27/51.44 assert (zenon_L347_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hb5 zenon_H10a zenon_H10e zenon_Hda zenon_H49 zenon_Hcc zenon_H9e zenon_H54 zenon_H95 zenon_H2c zenon_H1c zenon_Hab zenon_Hcf zenon_H4b zenon_He8 zenon_H8c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_H3d zenon_H19. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.27/51.44 apply (zenon_L15_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.27/51.44 apply (zenon_L344_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.27/51.44 apply (zenon_L346_); trivial. % 51.27/51.44 apply (zenon_L37_); trivial. % 51.27/51.44 (* end of lemma zenon_L347_ *) % 51.27/51.44 assert (zenon_L348_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (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 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hde zenon_H19 zenon_H3d zenon_Hb5 zenon_H8c zenon_He1 zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hcf zenon_H4b zenon_He8 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H9e zenon_Hea zenon_H41 zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.27/51.44 apply (zenon_L62_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.27/51.44 apply (zenon_L34_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.27/51.44 apply (zenon_L45_); trivial. % 51.27/51.44 apply (zenon_L46_); trivial. % 51.27/51.44 (* end of lemma zenon_L348_ *) % 51.27/51.44 assert (zenon_L349_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hde zenon_H19 zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H62 zenon_H7d zenon_Hbe zenon_H42 zenon_He8 zenon_H4b zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.27/51.44 apply (zenon_L67_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.27/51.44 apply (zenon_L34_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.27/51.44 apply (zenon_L45_); trivial. % 51.27/51.44 apply (zenon_L46_); trivial. % 51.27/51.44 (* end of lemma zenon_L349_ *) % 51.27/51.44 assert (zenon_L350_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_H90 zenon_H35 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_Hbe zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.44 apply (zenon_L47_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.44 apply (zenon_L17_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L349_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L350_ *) % 51.27/51.44 assert (zenon_L351_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.44 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hde zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H42 zenon_He8 zenon_H4b zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.27/51.44 apply (zenon_L39_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.27/51.44 apply (zenon_L350_); trivial. % 51.27/51.44 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.27/51.44 apply (zenon_L41_); trivial. % 51.27/51.44 apply (zenon_L24_); trivial. % 51.27/51.44 (* end of lemma zenon_L351_ *) % 51.27/51.44 assert (zenon_L352_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H46 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hde zenon_H3d zenon_He1 zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_He8 zenon_H4b zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.27/51.45 apply (zenon_L348_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.27/51.45 apply (zenon_L13_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.27/51.45 apply (zenon_L65_); trivial. % 51.27/51.45 apply (zenon_L351_); trivial. % 51.27/51.45 (* end of lemma zenon_L352_ *) % 51.27/51.45 assert (zenon_L353_ : (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H8c zenon_H1c zenon_Hc2 zenon_H90 zenon_H35 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_Hde zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_H2c8 zenon_H49 zenon_H2ff zenon_H10e zenon_H95 zenon_H41 zenon_H123 zenon_H311 zenon_H2ba zenon_H30b zenon_H1b zenon_H2d4 zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.27/51.45 apply (zenon_L57_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.27/51.45 apply (zenon_L42_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d | zenon_intro zenon_H2d5 ]. % 51.27/51.45 apply (zenon_L4_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H104 | zenon_intro zenon_H2d6 ]. % 51.27/51.45 apply (zenon_L340_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H2bb | zenon_intro zenon_H46 ]. % 51.27/51.45 apply (zenon_L281_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H121 | zenon_intro zenon_H312 ]. % 51.27/51.45 apply (zenon_L343_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H10a | zenon_intro zenon_H313 ]. % 51.27/51.45 apply (zenon_L347_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H7c | zenon_intro zenon_He2 ]. % 51.27/51.45 apply (zenon_L332_); trivial. % 51.27/51.45 apply (zenon_L352_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L353_ *) % 51.27/51.45 assert (zenon_L354_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H8c zenon_He8 zenon_H4b zenon_Hcf zenon_Hab zenon_H1c zenon_H2c zenon_H95 zenon_H54 zenon_H9e zenon_H49 zenon_Hda zenon_H10e zenon_H10a zenon_Hb5 zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.27/51.45 apply (zenon_L57_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.27/51.45 apply (zenon_L42_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_L347_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L354_ *) % 51.27/51.45 assert (zenon_L355_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hb0 zenon_Hda zenon_H49 zenon_Hcc zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H19 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H96. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.27/51.45 apply (zenon_L59_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.27/51.45 apply (zenon_L33_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.27/51.45 apply (zenon_L34_); trivial. % 51.27/51.45 apply (zenon_L35_); trivial. % 51.27/51.45 (* end of lemma zenon_L355_ *) % 51.27/51.45 assert (zenon_L356_ : (~((e10) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H8c zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H304 zenon_H305 zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_He8 zenon_H4b zenon_Hcf zenon_H95 zenon_H10e zenon_Hb5 zenon_Hd3 zenon_Hde zenon_H123 zenon_H311 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hcc zenon_H49 zenon_Hda zenon_Hb0 zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.27/51.45 apply (zenon_L335_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H121 | zenon_intro zenon_H312 ]. % 51.27/51.45 apply (zenon_L342_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H10a | zenon_intro zenon_H313 ]. % 51.27/51.45 apply (zenon_L354_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H7c | zenon_intro zenon_He2 ]. % 51.27/51.45 apply (zenon_L334_); trivial. % 51.27/51.45 apply (zenon_L52_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_L355_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L356_ *) % 51.27/51.45 assert (zenon_L357_ : ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e11))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hbe zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H311 zenon_H123 zenon_Hde zenon_Hd3 zenon_Hb5 zenon_H10e zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H305 zenon_H304 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H8c zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.27/51.45 apply (zenon_L57_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.27/51.45 apply (zenon_L40_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_L356_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L357_ *) % 51.27/51.45 assert (zenon_L358_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e11) = (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H30b zenon_H2ba zenon_H2ff zenon_Hf8 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H8c zenon_H19 zenon_Hc2 zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_Haf zenon_H311 zenon_H123 zenon_Hde zenon_Hb5 zenon_H10e zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_Hb8 zenon_Hc8 zenon_H305 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H3d zenon_H2c zenon_H1c zenon_Hd3. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H314); [ zenon_intro zenon_H7c | zenon_intro zenon_H315 ]. % 51.27/51.45 apply (zenon_L341_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H316 ]. % 51.27/51.45 apply (zenon_L353_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H304 | zenon_intro zenon_Hd2 ]. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.27/51.45 apply (zenon_L39_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.27/51.45 apply (zenon_L357_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.27/51.45 apply (zenon_L41_); trivial. % 51.27/51.45 apply (zenon_L24_); trivial. % 51.27/51.45 apply (zenon_L45_); trivial. % 51.27/51.45 (* end of lemma zenon_L358_ *) % 51.27/51.45 assert (zenon_L359_ : ((op1 (e11) (e12)) = (e10)) -> ((op1 (e11) (e12)) = (e11)) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H126 zenon_H129 zenon_H8c. % 51.27/51.45 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H8d | zenon_intro zenon_H3a ]. % 51.27/51.45 cut (((e11) = (e11)) = ((e10) = (e11))). % 51.27/51.45 intro zenon_D_pnotp. % 51.27/51.45 apply zenon_H8c. % 51.27/51.45 rewrite <- zenon_D_pnotp. % 51.27/51.45 exact zenon_H8d. % 51.27/51.45 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.27/51.45 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 51.27/51.45 congruence. % 51.27/51.45 cut (((op1 (e11) (e12)) = (e10)) = ((e11) = (e10))). % 51.27/51.45 intro zenon_D_pnotp. % 51.27/51.45 apply zenon_H8e. % 51.27/51.45 rewrite <- zenon_D_pnotp. % 51.27/51.45 exact zenon_H126. % 51.27/51.45 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.27/51.45 cut (((op1 (e11) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H317]. % 51.27/51.45 congruence. % 51.27/51.45 exact (zenon_H317 zenon_H129). % 51.27/51.45 apply zenon_H32. apply refl_equal. % 51.27/51.45 apply zenon_H3a. apply refl_equal. % 51.27/51.45 apply zenon_H3a. apply refl_equal. % 51.27/51.45 (* end of lemma zenon_L359_ *) % 51.27/51.45 assert (zenon_L360_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3d zenon_Hb5 zenon_H4b zenon_H42 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_He1 zenon_He8 zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.27/51.45 apply (zenon_L39_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.27/51.45 apply (zenon_L94_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.27/51.45 apply (zenon_L41_); trivial. % 51.27/51.45 apply (zenon_L24_); trivial. % 51.27/51.45 (* end of lemma zenon_L360_ *) % 51.27/51.45 assert (zenon_L361_ : ((op1 (e10) (e13)) = (e12)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H49 zenon_H318 zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H90 zenon_H35 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_H46 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_He8 zenon_H4b. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.27/51.45 apply (zenon_L11_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.27/51.45 apply (zenon_L71_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.27/51.45 apply (zenon_L283_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.27/51.45 apply (zenon_L328_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.27/51.45 apply (zenon_L358_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.27/51.45 apply (zenon_L359_); trivial. % 51.27/51.45 apply (zenon_L33_); trivial. % 51.27/51.45 apply (zenon_L360_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.27/51.45 apply (zenon_L352_); trivial. % 51.27/51.45 apply (zenon_L57_); trivial. % 51.27/51.45 (* end of lemma zenon_L361_ *) % 51.27/51.45 assert (zenon_L362_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.45 do 0 intro. intros zenon_He1 zenon_H54 zenon_H51 zenon_H66 zenon_H62 zenon_H65 zenon_Hcc zenon_H49 zenon_Hda. % 51.27/51.45 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.27/51.45 apply (zenon_L48_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.27/51.45 apply (zenon_L18_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.27/51.45 apply (zenon_L20_); trivial. % 51.27/51.45 apply (zenon_L50_); trivial. % 51.27/51.45 (* end of lemma zenon_L362_ *) % 51.27/51.45 assert (zenon_L363_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hde zenon_Hcc zenon_H65 zenon_H62 zenon_H66 zenon_H51 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.27/51.45 apply (zenon_L362_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.27/51.45 apply (zenon_L34_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.27/51.45 apply (zenon_L45_); trivial. % 51.27/51.45 apply (zenon_L46_); trivial. % 51.27/51.45 (* end of lemma zenon_L363_ *) % 51.27/51.45 assert (zenon_L364_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e12)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H51 zenon_H66 zenon_H65 zenon_Hcc zenon_Hde zenon_H19 zenon_H8c. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.45 apply (zenon_L47_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.45 apply (zenon_L17_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.45 apply (zenon_L363_); trivial. % 51.27/51.45 apply (zenon_L24_); trivial. % 51.27/51.45 (* end of lemma zenon_L364_ *) % 51.27/51.45 assert (zenon_L365_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e12)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H46 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H3d zenon_H7d zenon_Hcf zenon_Hc2 zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H49 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H51 zenon_H65 zenon_Hcc zenon_Hde zenon_H19 zenon_H8c. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H31b); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H31c ]. % 51.27/51.45 apply (zenon_L39_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H31c); [ zenon_intro zenon_H114 | zenon_intro zenon_H31d ]. % 51.27/51.45 apply (zenon_L82_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_He8 | zenon_intro zenon_H66 ]. % 51.27/51.45 apply (zenon_L361_); trivial. % 51.27/51.45 apply (zenon_L364_); trivial. % 51.27/51.45 (* end of lemma zenon_L365_ *) % 51.27/51.45 assert (zenon_L366_ : ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e12)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H3d zenon_H7d zenon_Hcf zenon_Hc2 zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H49 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H51 zenon_H65 zenon_Hcc zenon_Hde zenon_H19 zenon_H8c. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d | zenon_intro zenon_H2d5 ]. % 51.27/51.45 apply (zenon_L4_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H104 | zenon_intro zenon_H2d6 ]. % 51.27/51.45 apply (zenon_L340_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H2bb | zenon_intro zenon_H46 ]. % 51.27/51.45 apply (zenon_L281_); trivial. % 51.27/51.45 apply (zenon_L365_); trivial. % 51.27/51.45 (* end of lemma zenon_L366_ *) % 51.27/51.45 assert (zenon_L367_ : (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H8c zenon_Hde zenon_H65 zenon_Hd3 zenon_H42 zenon_H35 zenon_H90 zenon_H318 zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_Hc2 zenon_Hcf zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H30b zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hcc zenon_H49 zenon_Hda zenon_Hb0 zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.27/51.45 apply (zenon_L335_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.27/51.45 apply (zenon_L366_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_L355_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L367_ *) % 51.27/51.45 assert (zenon_L368_ : (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e12)) = (e12)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H2db zenon_H126 zenon_Hbe zenon_H2ce zenon_He6 zenon_H72 zenon_Hf1 zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_Hc2 zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H35 zenon_H42 zenon_Hd3 zenon_H65 zenon_Hde zenon_H8c zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.27/51.45 apply (zenon_L339_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.27/51.45 apply (zenon_L42_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_L367_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L368_ *) % 51.27/51.45 assert (zenon_L369_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H31e zenon_H2be zenon_H8c zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H305 zenon_H7c zenon_Hb5 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H4b zenon_Hde zenon_H42 zenon_He1 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_H95 zenon_H49 zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.27/51.45 apply (zenon_L282_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.27/51.45 apply (zenon_L333_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.27/51.45 apply (zenon_L334_); trivial. % 51.27/51.45 apply (zenon_L338_); trivial. % 51.27/51.45 (* end of lemma zenon_L369_ *) % 51.27/51.45 assert (zenon_L370_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hf8 zenon_H33 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hcb zenon_Hb5 zenon_H4b zenon_Haf zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H72 zenon_H65 zenon_He6 zenon_H2ce zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.27/51.45 apply (zenon_L12_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.27/51.45 apply (zenon_L299_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.27/51.45 apply (zenon_L295_); trivial. % 51.27/51.45 apply (zenon_L320_); trivial. % 51.27/51.45 (* end of lemma zenon_L370_ *) % 51.27/51.45 assert (zenon_L371_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H2e1 zenon_H2ba zenon_Ha2 zenon_H12b zenon_H2ff zenon_H1c zenon_H7c zenon_H49 zenon_H2c zenon_Hbe zenon_H35. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.27/51.45 apply (zenon_L281_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.27/51.45 apply (zenon_L331_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.27/51.45 apply (zenon_L332_); trivial. % 51.27/51.45 apply (zenon_L308_); trivial. % 51.27/51.45 (* end of lemma zenon_L371_ *) % 51.27/51.45 assert (zenon_L372_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e13) (e12)) = (e13)) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hde zenon_H8c zenon_H19 zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_Hcc zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.27/51.45 apply (zenon_L52_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.27/51.45 apply (zenon_L34_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.27/51.45 apply (zenon_L45_); trivial. % 51.27/51.45 apply (zenon_L46_); trivial. % 51.27/51.45 (* end of lemma zenon_L372_ *) % 51.27/51.45 assert (zenon_L373_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H8c zenon_Hde zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hcc zenon_H49 zenon_Hda zenon_Hb0 zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.27/51.45 apply (zenon_L335_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.27/51.45 apply (zenon_L372_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_L355_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L373_ *) % 51.27/51.45 assert (zenon_L374_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.27/51.45 do 0 intro. intros zenon_Hcf zenon_H72 zenon_H65 zenon_H62 zenon_He6 zenon_H2ce zenon_Hbe zenon_H126 zenon_H2db zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_Hde zenon_H8c zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.27/51.45 apply (zenon_L304_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.27/51.45 apply (zenon_L42_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.27/51.45 apply (zenon_L373_); trivial. % 51.27/51.45 apply (zenon_L37_); trivial. % 51.27/51.45 (* end of lemma zenon_L374_ *) % 51.27/51.45 assert (zenon_L375_ : (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e12)) = (e12)) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.27/51.45 do 0 intro. intros zenon_H95 zenon_Hf1 zenon_H3d zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_Hde zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H2db zenon_H126 zenon_Hbe zenon_H2ce zenon_He6 zenon_H65 zenon_H72 zenon_Hcf zenon_H19 zenon_H8c. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.27/51.45 apply (zenon_L16_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.27/51.45 apply (zenon_L338_); trivial. % 51.27/51.45 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.27/51.45 apply (zenon_L374_); trivial. % 51.27/51.45 apply (zenon_L24_); trivial. % 51.27/51.45 (* end of lemma zenon_L375_ *) % 51.27/51.45 assert (zenon_L376_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H31e zenon_H2be zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H305 zenon_H7c zenon_H95 zenon_H3d zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_Hde zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H2db zenon_H126 zenon_Hbe zenon_H2ce zenon_He6 zenon_H65 zenon_H72 zenon_Hcf zenon_H19 zenon_H8c. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.46 apply (zenon_L282_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.46 apply (zenon_L371_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.46 apply (zenon_L334_); trivial. % 51.29/51.46 apply (zenon_L375_); trivial. % 51.29/51.46 (* end of lemma zenon_L376_ *) % 51.29/51.46 assert (zenon_L377_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_Hf8 zenon_H49 zenon_Hea zenon_He1 zenon_H7c zenon_H305 zenon_H2e1 zenon_H2ff zenon_H35 zenon_H2be zenon_H31e zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H50 zenon_H42. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.46 apply (zenon_L369_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.46 apply (zenon_L299_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.46 apply (zenon_L288_); trivial. % 51.29/51.46 apply (zenon_L17_); trivial. % 51.29/51.46 (* end of lemma zenon_L377_ *) % 51.29/51.46 assert (zenon_L378_ : ((op1 (e10) (e10)) = (e10)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H23 zenon_H31b zenon_H113 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hfb zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H318 zenon_H7d zenon_H2e0 zenon_Hf6 zenon_Haf zenon_H10e zenon_H90 zenon_H72 zenon_H54 zenon_He6 zenon_H2ce zenon_H2db zenon_Hb0 zenon_Hf8 zenon_H49 zenon_Hea zenon_He1 zenon_H7c zenon_H305 zenon_H2e1 zenon_H2ff zenon_H35 zenon_H2be zenon_H31e zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H42. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.46 apply (zenon_L317_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.46 apply (zenon_L12_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.46 apply (zenon_L283_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.46 apply (zenon_L328_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.46 apply (zenon_L282_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.46 apply (zenon_L333_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.46 apply (zenon_L334_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.46 apply (zenon_L39_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.46 apply (zenon_L368_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.46 apply (zenon_L41_); trivial. % 51.29/51.46 apply (zenon_L24_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.46 apply (zenon_L359_); trivial. % 51.29/51.46 apply (zenon_L33_); trivial. % 51.29/51.46 apply (zenon_L369_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.46 apply (zenon_L370_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.46 apply (zenon_L283_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.46 apply (zenon_L39_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.46 apply (zenon_L376_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.46 apply (zenon_L41_); trivial. % 51.29/51.46 apply (zenon_L24_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.46 apply (zenon_L299_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.46 apply (zenon_L295_); trivial. % 51.29/51.46 apply (zenon_L320_); trivial. % 51.29/51.46 apply (zenon_L377_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.46 apply (zenon_L322_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.46 apply (zenon_L283_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.46 apply (zenon_L324_); trivial. % 51.29/51.46 apply (zenon_L377_); trivial. % 51.29/51.46 (* end of lemma zenon_L378_ *) % 51.29/51.46 assert (zenon_L379_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H19 zenon_H3d zenon_Hb0 zenon_Hcc zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Haf zenon_H311 zenon_H123 zenon_Hde zenon_Hb5 zenon_H10e zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H305 zenon_H304 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H8c zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.46 apply (zenon_L356_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.46 apply (zenon_L34_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.46 apply (zenon_L45_); trivial. % 51.29/51.46 apply (zenon_L46_); trivial. % 51.29/51.46 (* end of lemma zenon_L379_ *) % 51.29/51.46 assert (zenon_L380_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H72 zenon_H65 zenon_H62 zenon_H49 zenon_He6 zenon_H2ce zenon_H126 zenon_H2db zenon_Hbe zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H8c zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H304 zenon_H305 zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_He8 zenon_H4b zenon_Hcf zenon_H95 zenon_H10e zenon_Hb5 zenon_Hde zenon_H123 zenon_H311 zenon_Haf zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hb0 zenon_H3d zenon_H19. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.46 apply (zenon_L304_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.46 apply (zenon_L40_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.46 apply (zenon_L379_); trivial. % 51.29/51.46 apply (zenon_L37_); trivial. % 51.29/51.46 (* end of lemma zenon_L380_ *) % 51.29/51.46 assert (zenon_L381_ : (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H3d zenon_Hb0 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Haf zenon_H311 zenon_H123 zenon_Hde zenon_Hb5 zenon_H10e zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H305 zenon_H304 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_Hbe zenon_H2db zenon_H126 zenon_H2ce zenon_He6 zenon_H49 zenon_H65 zenon_H72 zenon_H19 zenon_H8c. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.46 apply (zenon_L16_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.46 apply (zenon_L94_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.46 apply (zenon_L380_); trivial. % 51.29/51.46 apply (zenon_L24_); trivial. % 51.29/51.46 (* end of lemma zenon_L381_ *) % 51.29/51.46 assert (zenon_L382_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H72 zenon_H65 zenon_H49 zenon_He6 zenon_H2ce zenon_H126 zenon_H2db zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H304 zenon_H305 zenon_Hc8 zenon_Hb8 zenon_He8 zenon_H4b zenon_Hcf zenon_H95 zenon_H10e zenon_Hb5 zenon_Hde zenon_H123 zenon_H311 zenon_Haf zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hb0 zenon_H3d zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.46 apply (zenon_L39_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.46 apply (zenon_L381_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.46 apply (zenon_L41_); trivial. % 51.29/51.46 apply (zenon_L24_); trivial. % 51.29/51.46 (* end of lemma zenon_L382_ *) % 51.29/51.46 assert (zenon_L383_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_Hfb zenon_H23 zenon_H318 zenon_H2db zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H2ff zenon_H30d zenon_H314 zenon_H2e0 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H90 zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H3d zenon_He1 zenon_H54 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H2ce zenon_He6 zenon_H65 zenon_H72 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_He8 zenon_H4b. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.46 apply (zenon_L317_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.46 apply (zenon_L12_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.46 apply (zenon_L283_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.46 apply (zenon_L328_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H314); [ zenon_intro zenon_H7c | zenon_intro zenon_H315 ]. % 51.29/51.46 apply (zenon_L341_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H316 ]. % 51.29/51.46 apply (zenon_L353_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H304 | zenon_intro zenon_Hd2 ]. % 51.29/51.46 apply (zenon_L382_); trivial. % 51.29/51.46 apply (zenon_L45_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.46 apply (zenon_L359_); trivial. % 51.29/51.46 apply (zenon_L33_); trivial. % 51.29/51.46 apply (zenon_L360_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.46 apply (zenon_L348_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.46 apply (zenon_L299_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.46 apply (zenon_L65_); trivial. % 51.29/51.46 apply (zenon_L320_); trivial. % 51.29/51.46 apply (zenon_L57_); trivial. % 51.29/51.46 (* end of lemma zenon_L383_ *) % 51.29/51.46 assert (zenon_L384_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.46 do 0 intro. intros zenon_Hff zenon_Hf6 zenon_He8 zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H72 zenon_H65 zenon_H2ce zenon_H42 zenon_H49 zenon_H7d zenon_H54 zenon_He1 zenon_H3d zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H2db zenon_H318 zenon_H23 zenon_Hfb zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.46 apply (zenon_L11_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.46 apply (zenon_L361_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.46 apply (zenon_L383_); trivial. % 51.29/51.46 apply (zenon_L335_); trivial. % 51.29/51.46 (* end of lemma zenon_L384_ *) % 51.29/51.46 assert (zenon_L385_ : ((op1 (e10) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((e11) = (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H104 zenon_H46 zenon_H3d. % 51.29/51.46 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.29/51.46 cut (((e13) = (e13)) = ((e11) = (e13))). % 51.29/51.46 intro zenon_D_pnotp. % 51.29/51.46 apply zenon_H3d. % 51.29/51.46 rewrite <- zenon_D_pnotp. % 51.29/51.46 exact zenon_H3e. % 51.29/51.46 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.29/51.46 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 51.29/51.46 congruence. % 51.29/51.46 cut (((op1 (e10) (e11)) = (e11)) = ((e13) = (e11))). % 51.29/51.46 intro zenon_D_pnotp. % 51.29/51.46 apply zenon_H3f. % 51.29/51.46 rewrite <- zenon_D_pnotp. % 51.29/51.46 exact zenon_H104. % 51.29/51.46 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.29/51.46 cut (((op1 (e10) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2f0]. % 51.29/51.46 congruence. % 51.29/51.46 exact (zenon_H2f0 zenon_H46). % 51.29/51.46 apply zenon_H3a. apply refl_equal. % 51.29/51.46 apply zenon_H17. apply refl_equal. % 51.29/51.46 apply zenon_H17. apply refl_equal. % 51.29/51.46 (* end of lemma zenon_L385_ *) % 51.29/51.46 assert (zenon_L386_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.46 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H2db zenon_H126 zenon_H50 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.46 apply (zenon_L39_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.46 apply (zenon_L303_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.46 apply (zenon_L41_); trivial. % 51.29/51.46 apply (zenon_L24_); trivial. % 51.29/51.46 (* end of lemma zenon_L386_ *) % 51.29/51.46 assert (zenon_L387_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H1c zenon_H321 zenon_Hbe zenon_H126 zenon_H19 zenon_H12c. % 51.29/51.46 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.29/51.46 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e11) (e12)) = (op1 (e12) (e12)))). % 51.29/51.46 intro zenon_D_pnotp. % 51.29/51.46 apply zenon_H12c. % 51.29/51.46 rewrite <- zenon_D_pnotp. % 51.29/51.46 exact zenon_H99. % 51.29/51.46 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.29/51.46 cut (((op1 (e12) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 51.29/51.46 congruence. % 51.29/51.46 cut (((e10) = (op1 (e13) (op1 (e13) (e13)))) = ((op1 (e12) (e12)) = (op1 (e11) (e12)))). % 51.29/51.46 intro zenon_D_pnotp. % 51.29/51.46 apply zenon_H12d. % 51.29/51.46 rewrite <- zenon_D_pnotp. % 51.29/51.46 exact zenon_H1c. % 51.29/51.46 cut (((op1 (e13) (op1 (e13) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 51.29/51.46 cut (((e10) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H322]. % 51.29/51.46 congruence. % 51.29/51.46 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.29/51.46 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e10) = (op1 (e12) (e12)))). % 51.29/51.46 intro zenon_D_pnotp. % 51.29/51.46 apply zenon_H322. % 51.29/51.46 rewrite <- zenon_D_pnotp. % 51.29/51.46 exact zenon_H99. % 51.29/51.46 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.29/51.46 cut (((op1 (e12) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H323]. % 51.29/51.46 congruence. % 51.29/51.46 exact (zenon_H323 zenon_H321). % 51.29/51.46 apply zenon_H9a. apply refl_equal. % 51.29/51.46 apply zenon_H9a. apply refl_equal. % 51.29/51.46 apply (zenon_L302_); trivial. % 51.29/51.46 apply zenon_H9a. apply refl_equal. % 51.29/51.46 apply zenon_H9a. apply refl_equal. % 51.29/51.46 (* end of lemma zenon_L387_ *) % 51.29/51.46 assert (zenon_L388_ : (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> False). % 51.29/51.46 do 0 intro. intros zenon_H131 zenon_H12c zenon_Hbe zenon_H321 zenon_H108 zenon_H128 zenon_H8c zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H19 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H96. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H126 | zenon_intro zenon_H132 ]. % 51.29/51.46 apply (zenon_L387_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H129 | zenon_intro zenon_H133 ]. % 51.29/51.46 apply (zenon_L101_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H12b | zenon_intro zenon_Ha3 ]. % 51.29/51.46 apply (zenon_L333_); trivial. % 51.29/51.46 apply (zenon_L36_); trivial. % 51.29/51.46 (* end of lemma zenon_L388_ *) % 51.29/51.46 assert (zenon_L389_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H42 zenon_H50 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H8c zenon_H128 zenon_H108 zenon_H321 zenon_Hbe zenon_H12c zenon_H131 zenon_H3d zenon_H19. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.46 apply (zenon_L15_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.46 apply (zenon_L17_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.46 apply (zenon_L388_); trivial. % 51.29/51.46 apply (zenon_L37_); trivial. % 51.29/51.46 (* end of lemma zenon_L389_ *) % 51.29/51.46 assert (zenon_L390_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_Hcf zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_Haf zenon_H50 zenon_H131 zenon_Hbe zenon_H321 zenon_H1c zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_H8c zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.46 apply (zenon_L389_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.46 apply (zenon_L40_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.46 apply (zenon_L335_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.46 apply (zenon_L372_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H126 | zenon_intro zenon_H132 ]. % 51.29/51.46 apply (zenon_L387_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H129 | zenon_intro zenon_H133 ]. % 51.29/51.46 apply (zenon_L101_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H12b | zenon_intro zenon_Ha3 ]. % 51.29/51.46 apply (zenon_L103_); trivial. % 51.29/51.46 apply (zenon_L43_); trivial. % 51.29/51.46 apply (zenon_L37_); trivial. % 51.29/51.46 apply (zenon_L37_); trivial. % 51.29/51.46 (* end of lemma zenon_L390_ *) % 51.29/51.46 assert (zenon_L391_ : (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H3d zenon_Hb5 zenon_H4b zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_Hde zenon_Hcb zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_H321 zenon_H131 zenon_H50 zenon_Haf zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.46 apply (zenon_L39_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.46 apply (zenon_L390_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.46 apply (zenon_L41_); trivial. % 51.29/51.46 apply (zenon_L24_); trivial. % 51.29/51.46 (* end of lemma zenon_L391_ *) % 51.29/51.46 assert (zenon_L392_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H324 zenon_He6 zenon_H2db zenon_H8c zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_Haf zenon_H50 zenon_H131 zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H4b zenon_Hb5 zenon_H3d zenon_H1c zenon_H19 zenon_Hc2. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.29/51.46 apply (zenon_L56_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.29/51.46 apply (zenon_L386_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.29/51.46 apply (zenon_L391_); trivial. % 51.29/51.46 apply (zenon_L41_); trivial. % 51.29/51.46 (* end of lemma zenon_L392_ *) % 51.29/51.46 assert (zenon_L393_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_H3d zenon_Hb5 zenon_H4b zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_H8c zenon_Hde zenon_Hcb zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_H50 zenon_Haf zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H1c zenon_H19 zenon_Hc2. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.29/51.46 apply (zenon_L5_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.29/51.46 apply (zenon_L303_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.29/51.46 apply (zenon_L390_); trivial. % 51.29/51.46 apply (zenon_L41_); trivial. % 51.29/51.46 (* end of lemma zenon_L393_ *) % 51.29/51.46 assert (zenon_L394_ : ((op1 (e13) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_Hcc zenon_H62 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H8c zenon_Hde zenon_Hcb zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hc2 zenon_H3d zenon_H19. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.46 apply (zenon_L335_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.46 apply (zenon_L51_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.29/51.46 apply (zenon_L393_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.29/51.46 apply (zenon_L33_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.29/51.46 apply (zenon_L34_); trivial. % 51.29/51.46 apply (zenon_L35_); trivial. % 51.29/51.46 apply (zenon_L37_); trivial. % 51.29/51.46 (* end of lemma zenon_L394_ *) % 51.29/51.46 assert (zenon_L395_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.46 do 0 intro. intros zenon_H72 zenon_He6 zenon_H2ce zenon_H126 zenon_Hc2 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H131 zenon_Hbe zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_H8c zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H2db zenon_H23 zenon_H24 zenon_H324 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H62 zenon_H3d zenon_H19. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.46 apply (zenon_L304_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.46 apply (zenon_L42_); trivial. % 51.29/51.46 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.46 apply (zenon_L394_); trivial. % 51.29/51.46 apply (zenon_L37_); trivial. % 51.29/51.46 (* end of lemma zenon_L395_ *) % 51.29/51.46 assert (zenon_L396_ : (~((e11) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H3d zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_Hde zenon_Hcb zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hc2 zenon_H126 zenon_H2ce zenon_He6 zenon_H72 zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.47 apply (zenon_L47_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.47 apply (zenon_L392_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L395_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L396_ *) % 51.29/51.47 assert (zenon_L397_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H72 zenon_He6 zenon_H2ce zenon_H126 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H131 zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H2db zenon_H23 zenon_H24 zenon_H324 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H3d zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.47 apply (zenon_L39_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.47 apply (zenon_L396_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L397_ *) % 51.29/51.47 assert (zenon_L398_ : (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H8c zenon_H19 zenon_Hc2 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_Haf zenon_H50 zenon_H131 zenon_H321 zenon_H108 zenon_H128 zenon_H9e zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H4b zenon_Hb5 zenon_H3d zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L391_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 (* end of lemma zenon_L398_ *) % 51.29/51.47 assert (zenon_L399_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e11))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H324 zenon_He6 zenon_H2db zenon_H3d zenon_H131 zenon_H12c zenon_Hbe zenon_H108 zenon_H128 zenon_H8c zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H50 zenon_H42 zenon_H4b zenon_Hb5 zenon_H1c zenon_H19 zenon_Hc2. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.29/51.47 apply (zenon_L56_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.29/51.47 apply (zenon_L303_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.29/51.47 apply (zenon_L389_); trivial. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 (* end of lemma zenon_L399_ *) % 51.29/51.47 assert (zenon_L400_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H42 zenon_H50 zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_H35 zenon_H128 zenon_H108 zenon_H12c zenon_H131 zenon_H3d zenon_H2db zenon_He6 zenon_H324 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.47 apply (zenon_L39_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.47 apply (zenon_L399_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L400_ *) % 51.29/51.47 assert (zenon_L401_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H90 zenon_Hc2 zenon_H324 zenon_H3d zenon_H131 zenon_H12c zenon_H108 zenon_H128 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Ha2 zenon_H9e zenon_H95 zenon_Haf zenon_H42 zenon_H4b zenon_Hb5 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_He6 zenon_H2ce zenon_H2c zenon_H1c zenon_Hab zenon_Hbe zenon_H126 zenon_H2db zenon_Hb0 zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.47 apply (zenon_L16_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.47 apply (zenon_L400_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L304_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L401_ *) % 51.29/51.47 assert (zenon_L402_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hde zenon_H8c zenon_H19 zenon_Hb0 zenon_H2db zenon_H126 zenon_Hbe zenon_H2ce zenon_He6 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_Hb5 zenon_H4b zenon_H42 zenon_Haf zenon_H95 zenon_H9e zenon_Ha2 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_H35 zenon_H128 zenon_H108 zenon_H12c zenon_H131 zenon_H3d zenon_H324 zenon_Hc2 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L401_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 (* end of lemma zenon_L402_ *) % 51.29/51.47 assert (zenon_L403_ : (~((e11) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H3d zenon_H131 zenon_H12c zenon_H321 zenon_H108 zenon_H128 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H50 zenon_H42 zenon_H4b zenon_Hb5 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.47 apply (zenon_L39_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.47 apply (zenon_L389_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L403_ *) % 51.29/51.47 assert (zenon_L404_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_Hb5 zenon_H4b zenon_H42 zenon_H50 zenon_Haf zenon_H54 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_H35 zenon_H128 zenon_H108 zenon_H321 zenon_H12c zenon_H131 zenon_H3d zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L403_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 (* end of lemma zenon_L404_ *) % 51.29/51.47 assert (zenon_L405_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H3d zenon_H131 zenon_H12c zenon_H108 zenon_H128 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H54 zenon_Haf zenon_H50 zenon_H42 zenon_H4b zenon_Hb5 zenon_H8c zenon_Hde zenon_H1c zenon_H19 zenon_Hc2. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.29/51.47 apply (zenon_L5_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.29/51.47 apply (zenon_L386_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.29/51.47 apply (zenon_L404_); trivial. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 (* end of lemma zenon_L405_ *) % 51.29/51.47 assert (zenon_L406_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hff zenon_Hc2 zenon_H19 zenon_H8c zenon_Hb5 zenon_H42 zenon_Haf zenon_H54 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_H35 zenon_H128 zenon_H108 zenon_H12c zenon_H131 zenon_H3d zenon_H2db zenon_H23 zenon_H24 zenon_H324 zenon_H90 zenon_H72 zenon_H2ce zenon_H10e zenon_H2e0 zenon_H113 zenon_Hf6 zenon_H10b zenon_H2b zenon_Hfe zenon_H104 zenon_H105 zenon_H117 zenon_H7d zenon_Hcb zenon_He1 zenon_Hcf zenon_Hfb zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.47 apply (zenon_L317_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.47 apply (zenon_L385_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.47 apply (zenon_L317_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.47 apply (zenon_L328_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.47 apply (zenon_L83_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.47 apply (zenon_L283_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L397_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.29/51.47 apply (zenon_L56_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.29/51.47 apply (zenon_L386_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.29/51.47 apply (zenon_L398_); trivial. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.47 apply (zenon_L74_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.47 apply (zenon_L283_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.47 apply (zenon_L39_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.47 apply (zenon_L402_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 apply (zenon_L405_); trivial. % 51.29/51.47 apply (zenon_L335_); trivial. % 51.29/51.47 (* end of lemma zenon_L406_ *) % 51.29/51.47 assert (zenon_L407_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hfb zenon_H23 zenon_H108 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H90 zenon_H35 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_H46 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_He8 zenon_H4b. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.47 apply (zenon_L317_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.47 apply (zenon_L328_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.47 apply (zenon_L352_); trivial. % 51.29/51.47 apply (zenon_L57_); trivial. % 51.29/51.47 (* end of lemma zenon_L407_ *) % 51.29/51.47 assert (zenon_L408_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_Hcf zenon_He8 zenon_He1 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_H3d zenon_Hb8 zenon_Hc8 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L360_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 (* end of lemma zenon_L408_ *) % 51.29/51.47 assert (zenon_L409_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H2e0 zenon_H10e zenon_H54 zenon_H45 zenon_H104 zenon_H318 zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_Hcf zenon_He8 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_H3d zenon_Hb8 zenon_Hc8 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.47 apply (zenon_L12_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.47 apply (zenon_L283_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.47 apply (zenon_L328_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.47 apply (zenon_L340_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.47 apply (zenon_L359_); trivial. % 51.29/51.47 apply (zenon_L33_); trivial. % 51.29/51.47 apply (zenon_L408_); trivial. % 51.29/51.47 (* end of lemma zenon_L409_ *) % 51.29/51.47 assert (zenon_L410_ : (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e13)) -> False). % 51.29/51.47 do 0 intro. intros zenon_H131 zenon_Hbe zenon_H321 zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H96 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_H19 zenon_H1c zenon_Hc2 zenon_Hf3 zenon_Hcb zenon_Hcc. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H126 | zenon_intro zenon_H132 ]. % 51.29/51.47 apply (zenon_L387_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H129 | zenon_intro zenon_H133 ]. % 51.29/51.47 apply (zenon_L101_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H12b | zenon_intro zenon_Ha3 ]. % 51.29/51.47 apply (zenon_L104_); trivial. % 51.29/51.47 apply (zenon_L43_); trivial. % 51.29/51.47 (* end of lemma zenon_L410_ *) % 51.29/51.47 assert (zenon_L411_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (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) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hb5 zenon_H2c zenon_Hd3 zenon_Hab zenon_H4b zenon_Hde zenon_H7d zenon_H62 zenon_He2 zenon_H54 zenon_Hcc zenon_Hcb zenon_Hf3 zenon_Hc2 zenon_H1c zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_H321 zenon_Hbe zenon_H131 zenon_H3d zenon_H19. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.47 apply (zenon_L335_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.47 apply (zenon_L51_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.47 apply (zenon_L410_); trivial. % 51.29/51.47 apply (zenon_L37_); trivial. % 51.29/51.47 (* end of lemma zenon_L411_ *) % 51.29/51.47 assert (zenon_L412_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (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) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H324 zenon_He6 zenon_H2db zenon_H50 zenon_H3d zenon_Hb5 zenon_H2c zenon_Hd3 zenon_Hab zenon_H4b zenon_Hde zenon_H7d zenon_H62 zenon_He2 zenon_H54 zenon_Hcb zenon_Hf3 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H8c zenon_Hcf zenon_H1c zenon_H19 zenon_Hc2. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.29/51.47 apply (zenon_L56_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.29/51.47 apply (zenon_L303_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.47 apply (zenon_L57_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.47 apply (zenon_L42_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.47 apply (zenon_L411_); trivial. % 51.29/51.47 apply (zenon_L37_); trivial. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 (* end of lemma zenon_L412_ *) % 51.29/51.47 assert (zenon_L413_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hb0 zenon_Hc2 zenon_Hcf zenon_H8c zenon_H42 zenon_Hb8 zenon_Hc8 zenon_H131 zenon_Hbe zenon_H108 zenon_H128 zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_Hf3 zenon_Hcb zenon_He2 zenon_H62 zenon_H7d zenon_Hde zenon_H4b zenon_Hd3 zenon_Hb5 zenon_H2db zenon_He6 zenon_H324 zenon_Hab zenon_H1c zenon_H2c zenon_H95 zenon_H54 zenon_H9e zenon_H49 zenon_Hda zenon_H90 zenon_H35 zenon_H3d zenon_H19. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.47 apply (zenon_L57_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.47 apply (zenon_L42_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.47 apply (zenon_L335_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.47 apply (zenon_L52_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.29/51.47 apply (zenon_L412_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.29/51.47 apply (zenon_L33_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_L345_); trivial. % 51.29/51.47 apply (zenon_L37_); trivial. % 51.29/51.47 apply (zenon_L37_); trivial. % 51.29/51.47 (* end of lemma zenon_L413_ *) % 51.29/51.47 assert (zenon_L414_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (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) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H19 zenon_H3d zenon_H35 zenon_H90 zenon_H9e zenon_H54 zenon_H95 zenon_H324 zenon_He6 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hde zenon_H7d zenon_H62 zenon_He2 zenon_Hcb zenon_Hf3 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H8c zenon_Hcf zenon_Hc2 zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L413_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 (* end of lemma zenon_L414_ *) % 51.29/51.47 assert (zenon_L415_ : ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H126 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hb0 zenon_Hc2 zenon_Hcf zenon_H42 zenon_Hb8 zenon_Hc8 zenon_H131 zenon_Hbe zenon_H108 zenon_H128 zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_Hf3 zenon_Hcb zenon_He2 zenon_H7d zenon_Hde zenon_H4b zenon_Hb5 zenon_H2db zenon_He6 zenon_H324 zenon_H95 zenon_H54 zenon_H9e zenon_H90 zenon_H35 zenon_H3d zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.47 apply (zenon_L47_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.47 apply (zenon_L303_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L414_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L415_ *) % 51.29/51.47 assert (zenon_L416_ : (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (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) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H3d zenon_H35 zenon_H90 zenon_H9e zenon_H54 zenon_H95 zenon_H324 zenon_He6 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hde zenon_H7d zenon_He2 zenon_Hcb zenon_Hf3 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H128 zenon_H108 zenon_H131 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hcf zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H126 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.47 apply (zenon_L39_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.47 apply (zenon_L415_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L416_ *) % 51.29/51.47 assert (zenon_L417_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e13) (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) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_H8c zenon_Hde zenon_Hcc zenon_Hcb zenon_Hf3 zenon_Hc2 zenon_H1c zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_H321 zenon_Hbe zenon_H131 zenon_H3d zenon_H19. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.47 apply (zenon_L15_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.47 apply (zenon_L372_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.47 apply (zenon_L410_); trivial. % 51.29/51.47 apply (zenon_L37_); trivial. % 51.29/51.47 (* end of lemma zenon_L417_ *) % 51.29/51.47 assert (zenon_L418_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H131 zenon_Hbe zenon_H321 zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_H1c zenon_Hc2 zenon_Hf3 zenon_Hcb zenon_Hde zenon_H8c zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.47 apply (zenon_L57_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.47 apply (zenon_L42_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.47 apply (zenon_L417_); trivial. % 51.29/51.47 apply (zenon_L37_); trivial. % 51.29/51.47 (* end of lemma zenon_L418_ *) % 51.29/51.47 assert (zenon_L419_ : (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H3d zenon_Hb5 zenon_H4b zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_Hde zenon_Hcb zenon_Hf3 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_H321 zenon_H131 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.47 apply (zenon_L39_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.47 apply (zenon_L418_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L419_ *) % 51.29/51.47 assert (zenon_L420_ : (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (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) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H8c zenon_H19 zenon_Hc2 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H131 zenon_H321 zenon_H108 zenon_H128 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_Hf3 zenon_Hcb zenon_Hde zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H4b zenon_Hb5 zenon_H3d zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L419_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 (* end of lemma zenon_L420_ *) % 51.29/51.47 assert (zenon_L421_ : ((op1 (e12) (e10)) = (e11)) -> ((op1 (e12) (e10)) = (e13)) -> (~((e11) = (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H10a zenon_He2 zenon_H3d. % 51.29/51.47 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.29/51.47 cut (((e13) = (e13)) = ((e11) = (e13))). % 51.29/51.47 intro zenon_D_pnotp. % 51.29/51.47 apply zenon_H3d. % 51.29/51.47 rewrite <- zenon_D_pnotp. % 51.29/51.47 exact zenon_H3e. % 51.29/51.47 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.29/51.47 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 51.29/51.47 congruence. % 51.29/51.47 cut (((op1 (e12) (e10)) = (e11)) = ((e13) = (e11))). % 51.29/51.47 intro zenon_D_pnotp. % 51.29/51.47 apply zenon_H3f. % 51.29/51.47 rewrite <- zenon_D_pnotp. % 51.29/51.47 exact zenon_H10a. % 51.29/51.47 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.29/51.47 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 51.29/51.47 congruence. % 51.29/51.47 exact (zenon_H122 zenon_He2). % 51.29/51.47 apply zenon_H3a. apply refl_equal. % 51.29/51.47 apply zenon_H17. apply refl_equal. % 51.29/51.47 apply zenon_H17. apply refl_equal. % 51.29/51.47 (* end of lemma zenon_L421_ *) % 51.29/51.47 assert (zenon_L422_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H318 zenon_H10b zenon_H34 zenon_H104 zenon_H45 zenon_H8c zenon_H126 zenon_H54 zenon_H19. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.47 apply (zenon_L99_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.47 apply (zenon_L340_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.47 apply (zenon_L359_); trivial. % 51.29/51.47 apply (zenon_L33_); trivial. % 51.29/51.47 (* end of lemma zenon_L422_ *) % 51.29/51.47 assert (zenon_L423_ : ((op1 (e12) (e13)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> False). % 51.29/51.47 do 0 intro. intros zenon_H96 zenon_H49 zenon_H95 zenon_H66 zenon_H50 zenon_H65 zenon_Hbe zenon_H10a zenon_H10e zenon_He1 zenon_Hf1. % 51.29/51.47 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.29/51.47 apply (zenon_L27_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.29/51.47 apply (zenon_L29_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.29/51.47 apply (zenon_L76_); trivial. % 51.29/51.47 apply (zenon_L336_); trivial. % 51.29/51.47 (* end of lemma zenon_L423_ *) % 51.29/51.47 assert (zenon_L424_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H42 zenon_Hf1 zenon_He1 zenon_H10e zenon_H10a zenon_Hbe zenon_H65 zenon_H50 zenon_H66 zenon_H95 zenon_H49 zenon_H3d zenon_H19. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.47 apply (zenon_L15_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.47 apply (zenon_L17_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.47 apply (zenon_L423_); trivial. % 51.29/51.47 apply (zenon_L37_); trivial. % 51.29/51.47 (* end of lemma zenon_L424_ *) % 51.29/51.47 assert (zenon_L425_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.47 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3d zenon_H49 zenon_H95 zenon_H66 zenon_H50 zenon_H65 zenon_H10a zenon_H10e zenon_He1 zenon_Hf1 zenon_H42 zenon_H4b zenon_Hb5 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.47 apply (zenon_L39_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.47 apply (zenon_L424_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L24_); trivial. % 51.29/51.47 (* end of lemma zenon_L425_ *) % 51.29/51.47 assert (zenon_L426_ : (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (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) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((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)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e12) = (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H131 zenon_H128 zenon_H12c zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hcb zenon_H7d zenon_H90 zenon_H2db zenon_H24 zenon_H324 zenon_H117 zenon_H105 zenon_Hf8 zenon_Hff zenon_Haf zenon_Ha2 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H72 zenon_H2ce zenon_H4b zenon_H3d zenon_H2e0 zenon_H10e zenon_H54 zenon_H45 zenon_H104 zenon_H318 zenon_Hde zenon_H8c zenon_Hc2 zenon_Hcf zenon_He1 zenon_Hea zenon_H9e zenon_H42 zenon_Hb5 zenon_Hb8 zenon_Hc8 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H23 zenon_Hfb zenon_H10b zenon_Hfe zenon_H2b zenon_Hb0 zenon_Hf6 zenon_H327 zenon_H35 zenon_H95 zenon_H65 zenon_H113 zenon_H19. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.29/51.47 apply (zenon_L73_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.29/51.47 apply (zenon_L7_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.29/51.47 apply (zenon_L99_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.29/51.47 apply (zenon_L406_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.47 apply (zenon_L317_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.47 apply (zenon_L407_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.47 apply (zenon_L317_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.47 apply (zenon_L409_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.47 apply (zenon_L83_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.47 apply (zenon_L283_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.47 apply (zenon_L416_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.29/51.47 apply (zenon_L5_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.29/51.47 apply (zenon_L386_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.29/51.47 apply (zenon_L420_); trivial. % 51.29/51.47 apply (zenon_L41_); trivial. % 51.29/51.47 apply (zenon_L57_); trivial. % 51.29/51.47 apply (zenon_L335_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.29/51.47 apply (zenon_L7_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.47 apply (zenon_L317_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.47 apply (zenon_L86_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.47 apply (zenon_L421_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.47 apply (zenon_L81_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.47 apply (zenon_L283_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.47 apply (zenon_L422_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.29/51.47 apply (zenon_L57_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.29/51.47 apply (zenon_L309_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.47 apply (zenon_L425_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.47 apply (zenon_L34_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.47 apply (zenon_L45_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 apply (zenon_L46_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.29/51.47 apply (zenon_L75_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.47 apply (zenon_L317_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.47 apply (zenon_L409_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.47 apply (zenon_L421_); trivial. % 51.29/51.47 apply (zenon_L57_); trivial. % 51.29/51.47 apply (zenon_L82_); trivial. % 51.29/51.47 (* end of lemma zenon_L426_ *) % 51.29/51.47 assert (zenon_L427_ : ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e13)) -> (~((e11) = (e13))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H11a zenon_He6 zenon_H3d. % 51.29/51.47 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.29/51.47 cut (((e13) = (e13)) = ((e11) = (e13))). % 51.29/51.47 intro zenon_D_pnotp. % 51.29/51.47 apply zenon_H3d. % 51.29/51.47 rewrite <- zenon_D_pnotp. % 51.29/51.47 exact zenon_H3e. % 51.29/51.47 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.29/51.47 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 51.29/51.47 congruence. % 51.29/51.47 cut (((op1 (e10) (e12)) = (e11)) = ((e13) = (e11))). % 51.29/51.47 intro zenon_D_pnotp. % 51.29/51.47 apply zenon_H3f. % 51.29/51.47 rewrite <- zenon_D_pnotp. % 51.29/51.47 exact zenon_H11a. % 51.29/51.47 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.29/51.47 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 51.29/51.47 congruence. % 51.29/51.47 exact (zenon_He7 zenon_He6). % 51.29/51.47 apply zenon_H3a. apply refl_equal. % 51.29/51.47 apply zenon_H17. apply refl_equal. % 51.29/51.47 apply zenon_H17. apply refl_equal. % 51.29/51.47 (* end of lemma zenon_L427_ *) % 51.29/51.47 assert (zenon_L428_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((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))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.47 do 0 intro. intros zenon_H13b zenon_H32a zenon_H2ba zenon_H2be zenon_H14e zenon_H2e7 zenon_H14 zenon_H13 zenon_H244 zenon_H2ea zenon_H2e9 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ff zenon_H2ce zenon_H2e0 zenon_H318 zenon_H327 zenon_H2d1 zenon_H2c9 zenon_H2c5 zenon_H31b zenon_H31e zenon_H2d4 zenon_H314 zenon_H30d zenon_H311 zenon_H305 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.29/51.47 apply (zenon_L7_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.29/51.47 apply (zenon_L281_); trivial. % 51.29/51.47 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.29/51.48 apply (zenon_L282_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.29/51.48 apply (zenon_L7_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.29/51.48 apply (zenon_L325_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.48 apply (zenon_L317_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.48 apply (zenon_L327_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.48 apply (zenon_L378_); trivial. % 51.29/51.48 apply (zenon_L335_); trivial. % 51.29/51.48 apply (zenon_L384_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.29/51.48 apply (zenon_L426_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.29/51.48 apply (zenon_L7_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.29/51.48 apply (zenon_L281_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.29/51.48 apply (zenon_L282_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.48 apply (zenon_L317_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.48 apply (zenon_L327_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.48 apply (zenon_L427_); trivial. % 51.29/51.48 apply (zenon_L15_); trivial. % 51.29/51.48 apply (zenon_L85_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.29/51.48 apply (zenon_L4_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.29/51.48 apply (zenon_L109_); trivial. % 51.29/51.48 apply (zenon_L47_); trivial. % 51.29/51.48 (* end of lemma zenon_L428_ *) % 51.29/51.48 assert (zenon_L429_ : ((op2 (e20) (e22)) = (e21)) -> ((op2 (e20) (e22)) = (e23)) -> (~((e21) = (e23))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H293 zenon_H256 zenon_H1f7. % 51.29/51.48 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.29/51.48 cut (((e23) = (e23)) = ((e21) = (e23))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H1f7. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H1ad. % 51.29/51.48 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.29/51.48 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 51.29/51.48 congruence. % 51.29/51.48 cut (((op2 (e20) (e22)) = (e21)) = ((e23) = (e21))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H239. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H293. % 51.29/51.48 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 51.29/51.48 cut (((op2 (e20) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H257 zenon_H256). % 51.29/51.48 apply zenon_H1f6. apply refl_equal. % 51.29/51.48 apply zenon_H14c. apply refl_equal. % 51.29/51.48 apply zenon_H14c. apply refl_equal. % 51.29/51.48 (* end of lemma zenon_L429_ *) % 51.29/51.48 assert (zenon_L430_ : (~((op1 (e13) (e13)) = (op1 (op1 (e10) (e11)) (op1 (e10) (e11))))) -> ((op1 (e10) (e11)) = (e13)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H32d zenon_H46. % 51.29/51.48 cut (((e13) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H32e]. % 51.29/51.48 cut (((e13) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H32e]. % 51.29/51.48 congruence. % 51.29/51.48 apply zenon_H32e. apply sym_equal. exact zenon_H46. % 51.29/51.48 apply zenon_H32e. apply sym_equal. exact zenon_H46. % 51.29/51.48 (* end of lemma zenon_L430_ *) % 51.29/51.48 assert (zenon_L431_ : (~((op1 (e13) (e13)) = (op1 (e12) (e11)))) -> ((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e11)) = (e11)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H32f zenon_H83 zenon_H46 zenon_H330. % 51.29/51.48 cut (((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e11)) = ((op1 (e13) (e13)) = (op1 (e12) (e11)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H32f. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H83. % 51.29/51.48 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H331]. % 51.29/51.48 cut (((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H332]. % 51.29/51.48 congruence. % 51.29/51.48 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (op1 (e13) (e13)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H332. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H5b. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (op1 (e10) (e11)) (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H32d]. % 51.29/51.48 congruence. % 51.29/51.48 apply (zenon_L430_); trivial. % 51.29/51.48 apply zenon_H5c. apply refl_equal. % 51.29/51.48 apply zenon_H5c. apply refl_equal. % 51.29/51.48 apply zenon_H331. apply sym_equal. exact zenon_H330. % 51.29/51.48 (* end of lemma zenon_L431_ *) % 51.29/51.48 assert (zenon_L432_ : ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H46 zenon_H330 zenon_H30b zenon_H19 zenon_H2c9 zenon_H54 zenon_H51 zenon_H66 zenon_H62 zenon_H65 zenon_He1 zenon_Hf1. % 51.29/51.48 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.29/51.48 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 51.29/51.48 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 51.29/51.48 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H2c9. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H19. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H32f]. % 51.29/51.48 cut (((e11) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 51.29/51.48 congruence. % 51.29/51.48 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H7a | zenon_intro zenon_H7b ]. % 51.29/51.48 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e11) = (op1 (e11) (e11)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H30c. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H7a. % 51.29/51.48 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 51.29/51.48 cut (((op1 (e11) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H333]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H333 zenon_H30b). % 51.29/51.48 apply zenon_H7b. apply refl_equal. % 51.29/51.48 apply zenon_H7b. apply refl_equal. % 51.29/51.48 apply (zenon_L431_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.29/51.48 apply (zenon_L18_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.29/51.48 apply (zenon_L20_); trivial. % 51.29/51.48 apply (zenon_L336_); trivial. % 51.29/51.48 (* end of lemma zenon_L432_ *) % 51.29/51.48 assert (zenon_L433_ : ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hbe zenon_Hda zenon_H49 zenon_H96 zenon_H9e zenon_H54 zenon_H95 zenon_H2c zenon_H1c zenon_Hab zenon_Hcf zenon_H4b zenon_He8 zenon_H8c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.48 apply (zenon_L57_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.48 apply (zenon_L40_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L346_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L433_ *) % 51.29/51.48 assert (zenon_L434_ : (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H3d zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_Hc8 zenon_Hb8 zenon_H42 zenon_He8 zenon_H4b zenon_Hcf zenon_Hab zenon_H2c zenon_H95 zenon_H54 zenon_H9e zenon_H96 zenon_H49 zenon_Hda zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.48 apply (zenon_L39_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.48 apply (zenon_L433_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L41_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L434_ *) % 51.29/51.48 assert (zenon_L435_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_H96 zenon_H9e zenon_H54 zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_H3d zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.48 apply (zenon_L434_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.48 apply (zenon_L34_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.48 apply (zenon_L45_); trivial. % 51.29/51.48 apply (zenon_L46_); trivial. % 51.29/51.48 (* end of lemma zenon_L435_ *) % 51.29/51.48 assert (zenon_L436_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H327 zenon_H3d zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_H54 zenon_Hc2 zenon_H19 zenon_H8c zenon_H35 zenon_Hbe zenon_Hd3 zenon_Hab zenon_H95 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_H96 zenon_He1 zenon_Hde zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.29/51.48 apply (zenon_L435_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.29/51.48 apply (zenon_L308_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.48 apply (zenon_L337_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.48 apply (zenon_L34_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.48 apply (zenon_L45_); trivial. % 51.29/51.48 apply (zenon_L46_); trivial. % 51.29/51.48 apply (zenon_L46_); trivial. % 51.29/51.48 (* end of lemma zenon_L436_ *) % 51.29/51.48 assert (zenon_L437_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e13)) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hda zenon_Hde zenon_He1 zenon_H9e zenon_Hea zenon_H41 zenon_H95 zenon_Hd3 zenon_Hbe zenon_H35 zenon_H8c zenon_Hc2 zenon_Hcf zenon_H4b zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hb0 zenon_H3d zenon_H327 zenon_H19 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H96. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.29/51.48 apply (zenon_L436_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.29/51.48 apply (zenon_L33_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.29/51.48 apply (zenon_L34_); trivial. % 51.29/51.48 apply (zenon_L35_); trivial. % 51.29/51.48 (* end of lemma zenon_L437_ *) % 51.29/51.48 assert (zenon_L438_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((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 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hb5 zenon_H49 zenon_Hf1 zenon_H65 zenon_H62 zenon_H66 zenon_H2c9 zenon_H30b zenon_H330 zenon_H46 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H327 zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_Hc2 zenon_H8c zenon_H35 zenon_Hbe zenon_Hd3 zenon_H95 zenon_H41 zenon_Hea zenon_H9e zenon_He1 zenon_Hde zenon_Hda zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.48 apply (zenon_L15_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.48 apply (zenon_L432_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L437_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L438_ *) % 51.29/51.48 assert (zenon_L439_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e12)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H90 zenon_H3d zenon_Hda zenon_Hde zenon_He1 zenon_H9e zenon_Hea zenon_H41 zenon_H95 zenon_Hd3 zenon_Hbe zenon_H35 zenon_Hc2 zenon_Hcf zenon_H4b zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hb0 zenon_H327 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H46 zenon_H330 zenon_H30b zenon_H2c9 zenon_H66 zenon_H65 zenon_Hf1 zenon_H49 zenon_Hb5 zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.48 apply (zenon_L47_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.48 apply (zenon_L338_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L438_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L439_ *) % 51.29/51.48 assert (zenon_L440_ : ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hf1 zenon_H2c9 zenon_H330 zenon_H46 zenon_H327 zenon_Hbe zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_Hc2 zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H35 zenon_H42 zenon_Hd3 zenon_H65 zenon_Hde zenon_H8c zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.48 apply (zenon_L439_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.48 apply (zenon_L40_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L367_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L440_ *) % 51.29/51.48 assert (zenon_L441_ : (~((op1 (e13) (e13)) = (op1 (e10) (e12)))) -> ((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H334 zenon_H83 zenon_H46 zenon_H11a. % 51.29/51.48 cut (((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e11)) = ((op1 (e13) (e13)) = (op1 (e10) (e12)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H334. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H83. % 51.29/51.48 cut (((e11) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2cd]. % 51.29/51.48 cut (((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H332]. % 51.29/51.48 congruence. % 51.29/51.48 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H5b | zenon_intro zenon_H5c ]. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (op1 (e13) (e13)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H332. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H5b. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (op1 (e10) (e11)) (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H32d]. % 51.29/51.48 congruence. % 51.29/51.48 apply (zenon_L430_); trivial. % 51.29/51.48 apply zenon_H5c. apply refl_equal. % 51.29/51.48 apply zenon_H5c. apply refl_equal. % 51.29/51.48 apply zenon_H2cd. apply sym_equal. exact zenon_H11a. % 51.29/51.48 (* end of lemma zenon_L441_ *) % 51.29/51.48 assert (zenon_L442_ : (((op1 (op1 (e10) (e10)) (op1 (e10) (e10))) = (e10))/\(((op1 (op1 (e10) (e11)) (op1 (e10) (e11))) = (e11))/\(((op1 (op1 (e10) (e12)) (op1 (e10) (e12))) = (e12))/\((op1 (op1 (e10) (e13)) (op1 (e10) (e13))) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H7f zenon_H19 zenon_H335 zenon_H11a zenon_H46 zenon_H2ce. % 51.29/51.48 apply (zenon_and_s _ _ zenon_H7f). zenon_intro zenon_H81. zenon_intro zenon_H80. % 51.29/51.48 apply (zenon_and_s _ _ zenon_H80). zenon_intro zenon_H83. zenon_intro zenon_H82. % 51.29/51.48 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.29/51.48 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H2ce. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H99. % 51.29/51.48 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.29/51.48 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2cf]. % 51.29/51.48 congruence. % 51.29/51.48 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H2cf. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H19. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H334]. % 51.29/51.48 cut (((e11) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H336]. % 51.29/51.48 congruence. % 51.29/51.48 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H99 | zenon_intro zenon_H9a ]. % 51.29/51.48 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e11) = (op1 (e12) (e12)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H336. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H99. % 51.29/51.48 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 51.29/51.48 cut (((op1 (e12) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H337]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H337 zenon_H335). % 51.29/51.48 apply zenon_H9a. apply refl_equal. % 51.29/51.48 apply zenon_H9a. apply refl_equal. % 51.29/51.48 apply (zenon_L441_); trivial. % 51.29/51.48 apply zenon_H9a. apply refl_equal. % 51.29/51.48 apply zenon_H9a. apply refl_equal. % 51.29/51.48 (* end of lemma zenon_L442_ *) % 51.29/51.48 assert (zenon_L443_ : (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e12)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H2ce zenon_H46 zenon_H11a zenon_H335 zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19 zenon_H51. % 51.29/51.48 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.29/51.48 apply (zenon_L442_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.29/51.48 apply (zenon_L18_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.29/51.48 apply (zenon_L20_); trivial. % 51.29/51.48 apply (zenon_L22_); trivial. % 51.29/51.48 (* end of lemma zenon_L443_ *) % 51.29/51.48 assert (zenon_L444_ : (~((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H338 zenon_H49 zenon_H7c zenon_H1c zenon_H2c6 zenon_Hf1. % 51.29/51.48 cut (((op1 (e11) (e11)) = (e12)) = ((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e13) (e12)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H338. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H2c6. % 51.29/51.48 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 51.29/51.48 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H339]. % 51.29/51.48 congruence. % 51.29/51.48 elim (classic ((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [ zenon_intro zenon_H2f8 | zenon_intro zenon_H2f9 ]. % 51.29/51.48 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e11) (e11)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H339. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H2f8. % 51.29/51.48 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2f9]. % 51.29/51.48 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 51.29/51.48 congruence. % 51.29/51.48 apply (zenon_L330_); trivial. % 51.29/51.48 apply zenon_H2f9. apply refl_equal. % 51.29/51.48 apply zenon_H2f9. apply refl_equal. % 51.29/51.48 apply zenon_Hf2. apply sym_equal. exact zenon_Hf1. % 51.29/51.48 (* end of lemma zenon_L444_ *) % 51.29/51.48 assert (zenon_L445_ : (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e10) (e12)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H33a zenon_H2c zenon_H2bf zenon_Hf1 zenon_H49 zenon_H7c zenon_H1c zenon_H2c6. % 51.29/51.48 cut (((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) = ((op1 (e10) (e12)) = (op1 (e13) (e12)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H33a. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H2c. % 51.29/51.48 cut (((op1 (op1 (e13) (op1 (e13) (e13))) (e13)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H338]. % 51.29/51.48 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2c0]. % 51.29/51.48 congruence. % 51.29/51.48 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 51.29/51.48 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e12) = (op1 (e10) (e12)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H2c0. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H25. % 51.29/51.48 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 51.29/51.48 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2c1]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H2c1 zenon_H2bf). % 51.29/51.48 apply zenon_H26. apply refl_equal. % 51.29/51.48 apply zenon_H26. apply refl_equal. % 51.29/51.48 apply (zenon_L444_); trivial. % 51.29/51.48 (* end of lemma zenon_L445_ *) % 51.29/51.48 assert (zenon_L446_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H2d1 zenon_H8c zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H335 zenon_H46 zenon_H2c6 zenon_H1c zenon_H7c zenon_Hf1 zenon_H2c zenon_H33a zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19 zenon_H51. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H22 | zenon_intro zenon_H2d2 ]. % 51.29/51.48 apply (zenon_L25_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H11a | zenon_intro zenon_H2d3 ]. % 51.29/51.48 apply (zenon_L443_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H2bf | zenon_intro zenon_He6 ]. % 51.29/51.48 apply (zenon_L445_); trivial. % 51.29/51.48 apply (zenon_L291_); trivial. % 51.29/51.48 (* end of lemma zenon_L446_ *) % 51.29/51.48 assert (zenon_L447_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((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 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H31e zenon_H2be zenon_Ha2 zenon_H305 zenon_Hb5 zenon_H72 zenon_H65 zenon_H62 zenon_H66 zenon_H49 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H335 zenon_H90 zenon_H7d zenon_H2d1 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H327 zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_Hc2 zenon_H8c zenon_H35 zenon_Hbe zenon_Hd3 zenon_H95 zenon_H41 zenon_Hea zenon_H9e zenon_He1 zenon_Hde zenon_Hda zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.48 apply (zenon_L282_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.48 apply (zenon_L331_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.48 apply (zenon_L334_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.48 apply (zenon_L335_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.48 apply (zenon_L446_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L437_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L447_ *) % 51.29/51.48 assert (zenon_L448_ : ((op1 (e13) (e12)) = (e12)) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hf1 zenon_H3d zenon_Hda zenon_Hde zenon_He1 zenon_H9e zenon_Hea zenon_H41 zenon_H95 zenon_Hd3 zenon_Hbe zenon_H35 zenon_Hc2 zenon_Hcf zenon_H4b zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hb0 zenon_H327 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H2d1 zenon_H7d zenon_H90 zenon_H335 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H49 zenon_H66 zenon_H65 zenon_H72 zenon_Hb5 zenon_H305 zenon_Ha2 zenon_H2be zenon_H31e zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.48 apply (zenon_L47_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.48 apply (zenon_L338_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L447_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L448_ *) % 51.29/51.48 assert (zenon_L449_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((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 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H31e zenon_H2be zenon_Ha2 zenon_H305 zenon_Hb5 zenon_H72 zenon_H65 zenon_H66 zenon_H49 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H335 zenon_H90 zenon_H7d zenon_H2d1 zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H327 zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_H35 zenon_Hd3 zenon_H95 zenon_H41 zenon_Hea zenon_H9e zenon_He1 zenon_Hde zenon_Hda zenon_H3d zenon_Hf1 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.48 apply (zenon_L39_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.48 apply (zenon_L448_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L41_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L449_ *) % 51.29/51.48 assert (zenon_L450_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H327 zenon_H2d1 zenon_H335 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hbe zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_Hc2 zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H35 zenon_H42 zenon_Hd3 zenon_H65 zenon_Hde zenon_H8c zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.48 apply (zenon_L282_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.48 apply (zenon_L331_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.48 apply (zenon_L334_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.48 apply (zenon_L449_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.48 apply (zenon_L40_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L367_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L450_ *) % 51.29/51.48 assert (zenon_L451_ : (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H3d zenon_Hde zenon_H65 zenon_Hd3 zenon_H42 zenon_H35 zenon_H90 zenon_H318 zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_Hcf zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H30b zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_Hb0 zenon_H31e zenon_H2be zenon_Ha2 zenon_H72 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H335 zenon_H2d1 zenon_H327 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.48 apply (zenon_L39_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.48 apply (zenon_L450_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L41_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L451_ *) % 51.29/51.48 assert (zenon_L452_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e13)) = (e11)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H9e zenon_H19 zenon_H33b. % 51.29/51.48 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H9e. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H19. % 51.29/51.48 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.29/51.48 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H33c]. % 51.29/51.48 congruence. % 51.29/51.48 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hd4 | zenon_intro zenon_Hd5 ]. % 51.29/51.48 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e11) = (op1 (e12) (e13)))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H33c. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_Hd4. % 51.29/51.48 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 51.29/51.48 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H33d]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H33d zenon_H33b). % 51.29/51.48 apply zenon_Hd5. apply refl_equal. % 51.29/51.48 apply zenon_Hd5. apply refl_equal. % 51.29/51.48 apply zenon_H5c. apply refl_equal. % 51.29/51.48 (* end of lemma zenon_L452_ *) % 51.29/51.48 assert (zenon_L453_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H33e zenon_H10b zenon_H2c9 zenon_H2e1 zenon_H8c zenon_H1c zenon_Hc2 zenon_H327 zenon_H2d1 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hb0 zenon_Hda zenon_H49 zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H35 zenon_H42 zenon_Hd3 zenon_H65 zenon_Hde zenon_H3d zenon_H9e zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.29/51.48 apply (zenon_L75_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.48 apply (zenon_L282_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.48 apply (zenon_L333_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.48 apply (zenon_L334_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.48 apply (zenon_L39_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.48 apply (zenon_L440_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L41_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.29/51.48 apply (zenon_L451_); trivial. % 51.29/51.48 apply (zenon_L452_); trivial. % 51.29/51.48 (* end of lemma zenon_L453_ *) % 51.29/51.48 assert (zenon_L454_ : ((op1 (e11) (e12)) = (e10)) -> ((op1 (e11) (e12)) = (e12)) -> (~((e10) = (e12))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H126 zenon_H12b zenon_H35. % 51.29/51.48 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.29/51.48 cut (((e12) = (e12)) = ((e10) = (e12))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H35. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H36. % 51.29/51.48 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.29/51.48 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 51.29/51.48 congruence. % 51.29/51.48 cut (((op1 (e11) (e12)) = (e10)) = ((e12) = (e10))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H38. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H126. % 51.29/51.48 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 51.29/51.48 cut (((op1 (e11) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2fe]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H2fe zenon_H12b). % 51.29/51.48 apply zenon_H32. apply refl_equal. % 51.29/51.48 apply zenon_H37. apply refl_equal. % 51.29/51.48 apply zenon_H37. apply refl_equal. % 51.29/51.48 (* end of lemma zenon_L454_ *) % 51.29/51.48 assert (zenon_L455_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e10) = (e12))) -> ((op1 (e11) (e12)) = (e10)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H341 zenon_H23 zenon_H2db zenon_H105 zenon_H125 zenon_H24 zenon_H2c5 zenon_Hff zenon_H19 zenon_H9e zenon_H3d zenon_Hde zenon_H65 zenon_Hd3 zenon_H42 zenon_H90 zenon_H318 zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_Hcf zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H30b zenon_Haf zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H49 zenon_Hda zenon_Hb0 zenon_H31e zenon_H2be zenon_Ha2 zenon_H72 zenon_H2ce zenon_H33a zenon_H7c zenon_H46 zenon_H2d1 zenon_H327 zenon_Hc2 zenon_H8c zenon_H2e1 zenon_H2c9 zenon_H10b zenon_H33e zenon_H35 zenon_H126 zenon_H2c zenon_H1c zenon_Hab. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.48 apply (zenon_L325_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.48 apply (zenon_L453_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.48 apply (zenon_L454_); trivial. % 51.29/51.48 apply (zenon_L34_); trivial. % 51.29/51.48 (* end of lemma zenon_L455_ *) % 51.29/51.48 assert (zenon_L456_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_Hf1 zenon_He1 zenon_H62 zenon_H2c9 zenon_H30b zenon_H330 zenon_H46 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.48 apply (zenon_L15_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.48 apply (zenon_L432_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L36_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L456_ *) % 51.29/51.48 assert (zenon_L457_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H327 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H8c zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H19 zenon_H3d zenon_Hb0 zenon_Ha3 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_Haf zenon_H46 zenon_H330 zenon_H30b zenon_H2c9 zenon_H62 zenon_He1 zenon_H4b zenon_Hb5 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.29/51.48 apply (zenon_L65_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.29/51.48 apply (zenon_L309_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.29/51.48 apply (zenon_L456_); trivial. % 51.29/51.48 apply (zenon_L46_); trivial. % 51.29/51.48 (* end of lemma zenon_L457_ *) % 51.29/51.48 assert (zenon_L458_ : (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e12)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e12)) = (e13)) -> False). % 51.29/51.48 do 0 intro. intros zenon_H2ce zenon_H46 zenon_H11a zenon_H335 zenon_H54 zenon_H51 zenon_H66 zenon_H62 zenon_H65 zenon_Ha2 zenon_H19 zenon_Ha3. % 51.29/51.48 apply (zenon_or_s _ _ ax10); [ zenon_intro zenon_H7f | zenon_intro zenon_H7e ]. % 51.29/51.48 apply (zenon_L442_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H53 | zenon_intro zenon_H8a ]. % 51.29/51.48 apply (zenon_L18_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H8a); [ zenon_intro zenon_H64 | zenon_intro zenon_H71 ]. % 51.29/51.48 apply (zenon_L20_); trivial. % 51.29/51.48 apply (zenon_L31_); trivial. % 51.29/51.48 (* end of lemma zenon_L458_ *) % 51.29/51.48 assert (zenon_L459_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H90 zenon_H35 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_H42 zenon_Hb5 zenon_H4b zenon_H9e zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_Ha3 zenon_Ha2 zenon_H65 zenon_H66 zenon_H51 zenon_H54 zenon_H335 zenon_H11a zenon_H46 zenon_H2ce zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.48 apply (zenon_L47_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.48 apply (zenon_L288_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L458_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L459_ *) % 51.29/51.48 assert (zenon_L460_ : (~((e10) = (e11))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H8c zenon_H2ce zenon_H46 zenon_H11a zenon_H335 zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hcf zenon_H4b zenon_Hb5 zenon_H42 zenon_Hcb zenon_Hde zenon_Hc2 zenon_H35 zenon_H90 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.48 apply (zenon_L335_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.48 apply (zenon_L459_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L36_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L460_ *) % 51.29/51.48 assert (zenon_L461_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H33e zenon_H10b zenon_H7c zenon_He1 zenon_H62 zenon_H2c9 zenon_H30b zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H3d zenon_Hb0 zenon_Ha3 zenon_Ha2 zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H90 zenon_H35 zenon_Hc2 zenon_Hde zenon_Hcb zenon_H42 zenon_Hb5 zenon_H4b zenon_Hcf zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H11a zenon_H46 zenon_H2ce zenon_H8c zenon_H9e zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.29/51.48 apply (zenon_L75_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.29/51.48 apply (zenon_L457_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.29/51.48 apply (zenon_L460_); trivial. % 51.29/51.48 apply (zenon_L452_); trivial. % 51.29/51.48 (* end of lemma zenon_L461_ *) % 51.29/51.48 assert (zenon_L462_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H9e zenon_H8c zenon_H2ce zenon_H46 zenon_H11a zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hcf zenon_H4b zenon_Hb5 zenon_Hde zenon_Hc2 zenon_H35 zenon_H90 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H30b zenon_H2c9 zenon_H62 zenon_He1 zenon_H7c zenon_H10b zenon_H33e zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.48 apply (zenon_L461_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.48 apply (zenon_L40_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L43_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L462_ *) % 51.29/51.48 assert (zenon_L463_ : (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hbe zenon_H42 zenon_H33e zenon_H10b zenon_H7c zenon_He1 zenon_H2c9 zenon_H30b zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H90 zenon_H35 zenon_Hc2 zenon_Hde zenon_Hb5 zenon_H4b zenon_Hcf zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H11a zenon_H46 zenon_H2ce zenon_H9e zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.48 apply (zenon_L16_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.48 apply (zenon_L287_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L462_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L463_ *) % 51.29/51.48 assert (zenon_L464_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H9e zenon_H2ce zenon_H46 zenon_H11a zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hcf zenon_H4b zenon_Hb5 zenon_Hde zenon_H35 zenon_H90 zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H30b zenon_H2c9 zenon_He1 zenon_H7c zenon_H10b zenon_H33e zenon_H42 zenon_Ha3 zenon_Hcb zenon_H3d zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.48 apply (zenon_L39_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.48 apply (zenon_L463_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L41_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L464_ *) % 51.29/51.48 assert (zenon_L465_ : ((op1 (e11) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e13)) -> (~((e11) = (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H129 zenon_Ha3 zenon_H3d. % 51.29/51.48 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.29/51.48 cut (((e13) = (e13)) = ((e11) = (e13))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H3d. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H3e. % 51.29/51.48 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.29/51.48 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 51.29/51.48 congruence. % 51.29/51.48 cut (((op1 (e11) (e12)) = (e11)) = ((e13) = (e11))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H3f. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H129. % 51.29/51.48 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.29/51.48 cut (((op1 (e11) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H344 zenon_Ha3). % 51.29/51.48 apply zenon_H3a. apply refl_equal. % 51.29/51.48 apply zenon_H17. apply refl_equal. % 51.29/51.48 apply zenon_H17. apply refl_equal. % 51.29/51.48 (* end of lemma zenon_L465_ *) % 51.29/51.48 assert (zenon_L466_ : ((op1 (e11) (e12)) = (e12)) -> ((op1 (e11) (e12)) = (e13)) -> (~((e12) = (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H12b zenon_Ha3 zenon_H4b. % 51.29/51.48 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H3e | zenon_intro zenon_H17 ]. % 51.29/51.48 cut (((e13) = (e13)) = ((e12) = (e13))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H4b. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H3e. % 51.29/51.48 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 51.29/51.48 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 51.29/51.48 congruence. % 51.29/51.48 cut (((op1 (e11) (e12)) = (e12)) = ((e13) = (e12))). % 51.29/51.48 intro zenon_D_pnotp. % 51.29/51.48 apply zenon_H4c. % 51.29/51.48 rewrite <- zenon_D_pnotp. % 51.29/51.48 exact zenon_H12b. % 51.29/51.48 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.29/51.48 cut (((op1 (e11) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H344]. % 51.29/51.48 congruence. % 51.29/51.48 exact (zenon_H344 zenon_Ha3). % 51.29/51.48 apply zenon_H37. apply refl_equal. % 51.29/51.48 apply zenon_H17. apply refl_equal. % 51.29/51.48 apply zenon_H17. apply refl_equal. % 51.29/51.48 (* end of lemma zenon_L466_ *) % 51.29/51.48 assert (zenon_L467_ : ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e13) (e12)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.48 do 0 intro. intros zenon_H51 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_H2ce zenon_H33a zenon_H2c zenon_Hf1 zenon_H7c zenon_H1c zenon_H2c6 zenon_H46 zenon_H335 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H2d1 zenon_H19 zenon_H8c. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.48 apply (zenon_L16_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.48 apply (zenon_L17_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.48 apply (zenon_L446_); trivial. % 51.29/51.48 apply (zenon_L24_); trivial. % 51.29/51.48 (* end of lemma zenon_L467_ *) % 51.29/51.48 assert (zenon_L468_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H8c zenon_H2d1 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H335 zenon_H46 zenon_H2c6 zenon_H7c zenon_Hf1 zenon_H33a zenon_H2ce zenon_H72 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.29/51.48 apply (zenon_L15_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.29/51.48 apply (zenon_L467_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.29/51.48 apply (zenon_L36_); trivial. % 51.29/51.48 apply (zenon_L37_); trivial. % 51.29/51.48 (* end of lemma zenon_L468_ *) % 51.29/51.48 assert (zenon_L469_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.48 do 0 intro. intros zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H72 zenon_H2ce zenon_H33a zenon_Hf1 zenon_H7c zenon_H2c6 zenon_H46 zenon_H335 zenon_H90 zenon_H35 zenon_H7d zenon_H2d1 zenon_H4b zenon_Hb5 zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.48 apply (zenon_L468_); trivial. % 51.29/51.48 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.49 apply (zenon_L42_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.49 apply (zenon_L43_); trivial. % 51.29/51.49 apply (zenon_L37_); trivial. % 51.29/51.49 (* end of lemma zenon_L469_ *) % 51.29/51.49 assert (zenon_L470_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H31e zenon_H2be zenon_H305 zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H72 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H335 zenon_H90 zenon_H35 zenon_H7d zenon_H2d1 zenon_H4b zenon_Hb5 zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.49 apply (zenon_L282_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.49 apply (zenon_L466_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.49 apply (zenon_L334_); trivial. % 51.29/51.49 apply (zenon_L469_); trivial. % 51.29/51.49 (* end of lemma zenon_L470_ *) % 51.29/51.49 assert (zenon_L471_ : (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (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 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H345 zenon_H33e zenon_H10b zenon_He1 zenon_H2c9 zenon_H30b zenon_Hf3 zenon_Hf0 zenon_H327 zenon_Hde zenon_Hd3 zenon_Hda zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H1c zenon_H8c zenon_Hb5 zenon_H4b zenon_H2d1 zenon_H7d zenon_H35 zenon_H90 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H305 zenon_H2be zenon_H31e zenon_Hec zenon_H19. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H11a | zenon_intro zenon_H346 ]. % 51.29/51.49 apply (zenon_L464_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H346); [ zenon_intro zenon_H129 | zenon_intro zenon_H347 ]. % 51.29/51.49 apply (zenon_L465_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H335 | zenon_intro zenon_Hed ]. % 51.29/51.49 apply (zenon_L470_); trivial. % 51.29/51.49 apply (zenon_L63_); trivial. % 51.29/51.49 (* end of lemma zenon_L471_ *) % 51.29/51.49 assert (zenon_L472_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.49 do 0 intro. intros zenon_Hcf zenon_Hf1 zenon_H65 zenon_H2c9 zenon_H30b zenon_H330 zenon_H46 zenon_H42 zenon_Hbe zenon_Hda zenon_H49 zenon_H7d zenon_H62 zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_H19. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.49 apply (zenon_L432_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.49 apply (zenon_L40_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.49 apply (zenon_L51_); trivial. % 51.29/51.49 apply (zenon_L37_); trivial. % 51.29/51.49 (* end of lemma zenon_L472_ *) % 51.29/51.49 assert (zenon_L473_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e12)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H90 zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_Hbe zenon_H42 zenon_H46 zenon_H330 zenon_H30b zenon_H2c9 zenon_H65 zenon_Hf1 zenon_Hcf zenon_H19 zenon_H8c. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.49 apply (zenon_L47_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.49 apply (zenon_L17_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.49 apply (zenon_L472_); trivial. % 51.29/51.49 apply (zenon_L24_); trivial. % 51.29/51.49 (* end of lemma zenon_L473_ *) % 51.29/51.49 assert (zenon_L474_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H31e zenon_H2be zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H305 zenon_H7c zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H65 zenon_H2c9 zenon_H30b zenon_H330 zenon_H46 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.49 apply (zenon_L282_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.49 apply (zenon_L333_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.49 apply (zenon_L334_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.49 apply (zenon_L39_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.49 apply (zenon_L473_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.49 apply (zenon_L41_); trivial. % 51.29/51.49 apply (zenon_L24_); trivial. % 51.29/51.49 (* end of lemma zenon_L474_ *) % 51.29/51.49 assert (zenon_L475_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H31e zenon_H2be zenon_Ha2 zenon_H305 zenon_H51 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H49 zenon_H2ce zenon_H33a zenon_H2c zenon_H7c zenon_H1c zenon_H2c6 zenon_H46 zenon_H335 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H2d1 zenon_H19 zenon_H8c. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.49 apply (zenon_L282_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.49 apply (zenon_L331_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.49 apply (zenon_L334_); trivial. % 51.29/51.49 apply (zenon_L467_); trivial. % 51.29/51.49 (* end of lemma zenon_L475_ *) % 51.29/51.49 assert (zenon_L476_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H2d1 zenon_H335 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hbe zenon_H8c zenon_Hde zenon_H65 zenon_H51 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H49 zenon_H318 zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_Hc2 zenon_Hcf zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H30b zenon_H3d zenon_H19. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.49 apply (zenon_L475_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.49 apply (zenon_L40_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.49 apply (zenon_L366_); trivial. % 51.29/51.49 apply (zenon_L37_); trivial. % 51.29/51.49 (* end of lemma zenon_L476_ *) % 51.29/51.49 assert (zenon_L477_ : (~((e11) = (e13))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H3d zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H49 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H51 zenon_H65 zenon_Hde zenon_H31e zenon_H2be zenon_Ha2 zenon_H72 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H335 zenon_H2d1 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.49 apply (zenon_L39_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.49 apply (zenon_L476_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.49 apply (zenon_L41_); trivial. % 51.29/51.49 apply (zenon_L24_); trivial. % 51.29/51.49 (* end of lemma zenon_L477_ *) % 51.29/51.49 assert (zenon_L478_ : (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((e11) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H105 zenon_H327 zenon_H10b zenon_H345 zenon_H33e zenon_He2 zenon_H2c9 zenon_H2e1 zenon_H8c zenon_H1c zenon_Hc2 zenon_H2d1 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hde zenon_H65 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H49 zenon_H318 zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_Hcf zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_Hea zenon_Hb0 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H30b zenon_H3d zenon_H9e zenon_H19. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.49 apply (zenon_L453_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.49 apply (zenon_L299_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.49 apply (zenon_L471_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.29/51.49 apply (zenon_L421_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.29/51.49 apply (zenon_L474_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.29/51.49 apply (zenon_L477_); trivial. % 51.29/51.49 apply (zenon_L452_); trivial. % 51.29/51.49 (* end of lemma zenon_L478_ *) % 51.29/51.49 assert (zenon_L479_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H341 zenon_H2c5 zenon_H2db zenon_H23 zenon_H24 zenon_H125 zenon_H9e zenon_H3d zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H42 zenon_Hda zenon_Hd3 zenon_He1 zenon_H54 zenon_H65 zenon_Hde zenon_H31e zenon_H2be zenon_H72 zenon_H2ce zenon_H33a zenon_H46 zenon_H2d1 zenon_H2c9 zenon_He2 zenon_H33e zenon_H345 zenon_H10b zenon_H327 zenon_H105 zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H49 zenon_H7c zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H2c zenon_H1c zenon_Hab. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.49 apply (zenon_L316_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.49 apply (zenon_L478_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.49 apply (zenon_L333_); trivial. % 51.29/51.49 apply (zenon_L34_); trivial. % 51.29/51.49 (* end of lemma zenon_L479_ *) % 51.29/51.49 assert (zenon_L480_ : ((op1 (e11) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e12)) -> (~((e11) = (e12))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H129 zenon_H12b zenon_H10b. % 51.29/51.49 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 51.29/51.49 cut (((e12) = (e12)) = ((e11) = (e12))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H10b. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H36. % 51.29/51.49 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 51.29/51.49 cut (((e12) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 51.29/51.49 congruence. % 51.29/51.49 cut (((op1 (e11) (e12)) = (e11)) = ((e12) = (e11))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H10c. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H129. % 51.29/51.49 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 51.29/51.49 cut (((op1 (e11) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2fe]. % 51.29/51.49 congruence. % 51.29/51.49 exact (zenon_H2fe zenon_H12b). % 51.29/51.49 apply zenon_H3a. apply refl_equal. % 51.29/51.49 apply zenon_H37. apply refl_equal. % 51.29/51.49 apply zenon_H37. apply refl_equal. % 51.29/51.49 (* end of lemma zenon_L480_ *) % 51.29/51.49 assert (zenon_L481_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e11) = (e13))) -> ((op1 (e11) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e12)) = (e10)) -> ((op1 (e12) (e10)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.49 do 0 intro. intros zenon_Hf8 zenon_H33 zenon_H46 zenon_H45 zenon_H3d zenon_H129 zenon_H90 zenon_H35 zenon_H49 zenon_H42 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H7d zenon_H22 zenon_H7c zenon_H19 zenon_H8c. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.49 apply (zenon_L12_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.49 apply (zenon_L13_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.49 apply (zenon_L465_); trivial. % 51.29/51.49 apply (zenon_L25_); trivial. % 51.29/51.49 (* end of lemma zenon_L481_ *) % 51.29/51.49 assert (zenon_L482_ : (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False). % 51.29/51.49 do 0 intro. intros zenon_H125 zenon_H11a zenon_H129. % 51.29/51.49 cut (((op1 (e10) (e12)) = (e11)) = ((op1 (e10) (e12)) = (op1 (e11) (e12)))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H125. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H11a. % 51.29/51.49 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 51.29/51.49 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 51.29/51.49 congruence. % 51.29/51.49 apply zenon_H26. apply refl_equal. % 51.29/51.49 apply zenon_H12a. apply sym_equal. exact zenon_H129. % 51.29/51.49 (* end of lemma zenon_L482_ *) % 51.29/51.49 assert (zenon_L483_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e13)) -> False). % 51.29/51.49 do 0 intro. intros zenon_H2d1 zenon_H8c zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H45 zenon_H46 zenon_H33 zenon_Hf8 zenon_H129 zenon_H125 zenon_H2c6 zenon_H1c zenon_H7c zenon_Hf1 zenon_H2c zenon_H33a zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H62 zenon_H65 zenon_H72 zenon_H19 zenon_H51. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H22 | zenon_intro zenon_H2d2 ]. % 51.29/51.49 apply (zenon_L481_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H11a | zenon_intro zenon_H2d3 ]. % 51.29/51.49 apply (zenon_L482_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H2bf | zenon_intro zenon_He6 ]. % 51.29/51.49 apply (zenon_L445_); trivial. % 51.29/51.49 apply (zenon_L291_); trivial. % 51.29/51.49 (* end of lemma zenon_L483_ *) % 51.29/51.49 assert (zenon_L484_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e13) (e12)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e11)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.49 do 0 intro. intros zenon_Hcf zenon_H72 zenon_H65 zenon_H62 zenon_H2ce zenon_H33a zenon_H2c zenon_Hf1 zenon_H7c zenon_H2c6 zenon_H125 zenon_H129 zenon_Hf8 zenon_H33 zenon_H46 zenon_H45 zenon_H2d1 zenon_H1c zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H8c zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H19. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.49 apply (zenon_L483_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.49 apply (zenon_L42_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.49 apply (zenon_L52_); trivial. % 51.29/51.49 apply (zenon_L37_); trivial. % 51.29/51.49 (* end of lemma zenon_L484_ *) % 51.29/51.49 assert (zenon_L485_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> ((op1 (e11) (e12)) = (e11)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H341 zenon_H8c zenon_H19 zenon_Hcf zenon_H72 zenon_H65 zenon_H2ce zenon_H33a zenon_H7c zenon_H125 zenon_Hf8 zenon_H33 zenon_H46 zenon_H45 zenon_H2d1 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_He1 zenon_H54 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_Hde zenon_Hd3 zenon_H305 zenon_H2be zenon_H31e zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H10b zenon_H129 zenon_H2c zenon_H1c zenon_Hab. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.49 apply (zenon_L9_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.49 apply (zenon_L12_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.49 apply (zenon_L299_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.49 apply (zenon_L465_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.49 apply (zenon_L282_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.49 apply (zenon_L480_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.49 apply (zenon_L334_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.49 apply (zenon_L47_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.49 apply (zenon_L17_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.49 apply (zenon_L484_); trivial. % 51.29/51.49 apply (zenon_L24_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.49 apply (zenon_L480_); trivial. % 51.29/51.49 apply (zenon_L34_); trivial. % 51.29/51.49 (* end of lemma zenon_L485_ *) % 51.29/51.49 assert (zenon_L486_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H2e1 zenon_Ha2 zenon_H2ff zenon_H327 zenon_H345 zenon_H33e zenon_H2c9 zenon_H318 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H30d zenon_H314 zenon_Hfb zenon_Hf6 zenon_H2e0 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_Hb5 zenon_Hea zenon_Hb0 zenon_H4b zenon_H113 zenon_H31b zenon_H9e zenon_H24 zenon_H23 zenon_H2db zenon_H2c5 zenon_Hab zenon_H1c zenon_H2c zenon_H10b zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H31e zenon_H2be zenon_H305 zenon_Hd3 zenon_Hde zenon_H3d zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_He1 zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H2d1 zenon_H45 zenon_H46 zenon_H33 zenon_Hf8 zenon_H125 zenon_H7c zenon_H33a zenon_H2ce zenon_H65 zenon_H72 zenon_Hcf zenon_H8c zenon_H341 zenon_H54 zenon_H19. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.49 apply (zenon_L74_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.49 apply (zenon_L479_); trivial. % 51.29/51.49 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.49 apply (zenon_L485_); trivial. % 51.29/51.49 apply (zenon_L33_); trivial. % 51.29/51.49 (* end of lemma zenon_L486_ *) % 51.29/51.49 assert (zenon_L487_ : (~((h4 (e12)) = (e22))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H348 zenon_H349 zenon_H15e. % 51.29/51.49 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((h4 (e12)) = (e22))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H348. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H349. % 51.29/51.49 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H34a]. % 51.29/51.49 cut (((h4 (e12)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H34b]. % 51.29/51.49 congruence. % 51.29/51.49 apply zenon_H34b. apply refl_equal. % 51.29/51.49 apply zenon_H34a. apply sym_equal. exact zenon_H15e. % 51.29/51.49 (* end of lemma zenon_L487_ *) % 51.29/51.49 assert (zenon_L488_ : (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op1 (e10) (e12)) = (e11)) -> ((op2 (e20) (e22)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> False). % 51.29/51.49 do 0 intro. intros zenon_H34c zenon_H2e7 zenon_H11a zenon_H293 zenon_H14e zenon_H13 zenon_H14 zenon_H349 zenon_H15e. % 51.29/51.49 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H34c. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H2e7. % 51.29/51.49 cut (((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H34d]. % 51.29/51.49 cut (((h4 (e11)) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H34e]. % 51.29/51.49 congruence. % 51.29/51.49 elim (classic ((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [ zenon_intro zenon_H34f | zenon_intro zenon_H350 ]. % 51.29/51.49 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12)))) = ((h4 (e11)) = (h4 (op1 (e10) (e12))))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H34e. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H34f. % 51.29/51.49 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H350]. % 51.29/51.49 cut (((h4 (op1 (e10) (e12))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H351]. % 51.29/51.49 congruence. % 51.29/51.49 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 51.29/51.49 congruence. % 51.29/51.49 exact (zenon_H11b zenon_H11a). % 51.29/51.49 apply zenon_H350. apply refl_equal. % 51.29/51.49 apply zenon_H350. apply refl_equal. % 51.29/51.49 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H352 | zenon_intro zenon_H353 ]. % 51.29/51.49 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H34d. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H352. % 51.29/51.49 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H353]. % 51.29/51.49 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H354]. % 51.29/51.49 congruence. % 51.29/51.49 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H354. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H293. % 51.29/51.49 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 51.29/51.49 cut (((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H355]. % 51.29/51.49 congruence. % 51.29/51.49 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H352 | zenon_intro zenon_H353 ]. % 51.29/51.49 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))). % 51.29/51.49 intro zenon_D_pnotp. % 51.29/51.49 apply zenon_H355. % 51.29/51.49 rewrite <- zenon_D_pnotp. % 51.29/51.49 exact zenon_H352. % 51.29/51.49 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H353]. % 51.29/51.49 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H356]. % 51.29/51.49 congruence. % 51.29/51.49 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.29/51.49 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 51.29/51.49 congruence. % 51.29/51.49 apply (zenon_L1_); trivial. % 51.29/51.49 apply (zenon_L487_); trivial. % 51.29/51.49 apply zenon_H353. apply refl_equal. % 51.29/51.49 apply zenon_H353. apply refl_equal. % 51.29/51.49 exact (zenon_H243 zenon_H14e). % 51.29/51.49 apply zenon_H353. apply refl_equal. % 51.29/51.49 apply zenon_H353. apply refl_equal. % 51.29/51.49 (* end of lemma zenon_L488_ *) % 51.29/51.49 assert (zenon_L489_ : (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e22)) = (e21)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H345 zenon_H15e zenon_H349 zenon_H14 zenon_H13 zenon_H14e zenon_H293 zenon_H2e7 zenon_H34c zenon_H108 zenon_H128 zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H1c zenon_H8c zenon_Hb5 zenon_H4b zenon_H2d1 zenon_H7d zenon_H35 zenon_H90 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H305 zenon_H2be zenon_H31e zenon_Hec zenon_H19. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H11a | zenon_intro zenon_H346 ]. % 51.29/51.50 apply (zenon_L488_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H346); [ zenon_intro zenon_H129 | zenon_intro zenon_H347 ]. % 51.29/51.50 apply (zenon_L101_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H335 | zenon_intro zenon_Hed ]. % 51.29/51.50 apply (zenon_L470_); trivial. % 51.29/51.50 apply (zenon_L63_); trivial. % 51.29/51.50 (* end of lemma zenon_L489_ *) % 51.29/51.50 assert (zenon_L490_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H31e zenon_H2be zenon_Ha2 zenon_H305 zenon_Hcf zenon_H2d1 zenon_H335 zenon_H46 zenon_H2c6 zenon_H1c zenon_H7c zenon_H2c zenon_H33a zenon_H2ce zenon_H65 zenon_H72 zenon_Hbe zenon_H8c zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H19. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.50 apply (zenon_L282_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.50 apply (zenon_L331_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.50 apply (zenon_L334_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.50 apply (zenon_L467_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.50 apply (zenon_L40_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.50 apply (zenon_L52_); trivial. % 51.29/51.50 apply (zenon_L37_); trivial. % 51.29/51.50 (* end of lemma zenon_L490_ *) % 51.29/51.50 assert (zenon_L491_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e11)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H31e zenon_H2be zenon_Ha2 zenon_H2c6 zenon_H305 zenon_H1c zenon_H7c zenon_H2c zenon_H90 zenon_H35 zenon_H49 zenon_H42 zenon_He1 zenon_H65 zenon_H66 zenon_H51 zenon_H54 zenon_H2c9 zenon_H30b zenon_H330 zenon_H46 zenon_H19 zenon_H8c. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.50 apply (zenon_L282_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.50 apply (zenon_L331_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.50 apply (zenon_L334_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.50 apply (zenon_L16_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.50 apply (zenon_L17_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.50 apply (zenon_L432_); trivial. % 51.29/51.50 apply (zenon_L24_); trivial. % 51.29/51.50 (* end of lemma zenon_L491_ *) % 51.29/51.50 assert (zenon_L492_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H341 zenon_H9e zenon_H31e zenon_H2be zenon_H305 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H2ce zenon_H33a zenon_H46 zenon_H90 zenon_H42 zenon_H7d zenon_H2d1 zenon_He1 zenon_H2c9 zenon_H30b zenon_Hfe zenon_H2b zenon_H10b zenon_H3d zenon_Hb0 zenon_H33 zenon_Hf6 zenon_H10e zenon_Hda zenon_H4b zenon_Hcf zenon_H33e zenon_H345 zenon_Hf3 zenon_Hf0 zenon_H327 zenon_Hde zenon_Hd3 zenon_Hcb zenon_Hb5 zenon_Haf zenon_H95 zenon_Hec zenon_H45 zenon_Hf8 zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H49 zenon_H7c zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H2c zenon_H1c zenon_Hab. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.50 apply (zenon_L9_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.50 apply (zenon_L12_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.50 apply (zenon_L13_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.50 apply (zenon_L471_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.29/51.50 apply (zenon_L80_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.29/51.50 apply (zenon_L491_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.29/51.50 apply (zenon_L475_); trivial. % 51.29/51.50 apply (zenon_L452_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.50 apply (zenon_L333_); trivial. % 51.29/51.50 apply (zenon_L34_); trivial. % 51.29/51.50 (* end of lemma zenon_L492_ *) % 51.29/51.50 assert (zenon_L493_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> ((op1 (e11) (e12)) = (e11)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H341 zenon_Hb5 zenon_H4b zenon_H9e zenon_H95 zenon_H2e1 zenon_H2c5 zenon_H2db zenon_Hb0 zenon_H2c9 zenon_H23 zenon_H24 zenon_Hda zenon_Hd3 zenon_Hde zenon_Hcb zenon_Haf zenon_Hcf zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H10e zenon_H2e0 zenon_H8c zenon_H19 zenon_H2d1 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H45 zenon_H46 zenon_H33 zenon_Hf8 zenon_H125 zenon_H7c zenon_H33a zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H305 zenon_Ha2 zenon_H2be zenon_H31e zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H10b zenon_H129 zenon_H2c zenon_H1c zenon_Hab. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.50 apply (zenon_L315_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.50 apply (zenon_L12_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.50 apply (zenon_L299_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.50 apply (zenon_L465_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.50 apply (zenon_L282_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.50 apply (zenon_L331_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.50 apply (zenon_L334_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.50 apply (zenon_L16_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.50 apply (zenon_L17_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.50 apply (zenon_L483_); trivial. % 51.29/51.50 apply (zenon_L24_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.50 apply (zenon_L480_); trivial. % 51.29/51.50 apply (zenon_L34_); trivial. % 51.29/51.50 (* end of lemma zenon_L493_ *) % 51.29/51.50 assert (zenon_L494_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (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 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H318 zenon_H2ff zenon_Hec zenon_H327 zenon_Hf0 zenon_Hf3 zenon_H345 zenon_H33e zenon_Hf6 zenon_H2b zenon_Hfe zenon_He1 zenon_Hab zenon_H1c zenon_H2c zenon_H10b zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H31e zenon_H2be zenon_Ha2 zenon_H305 zenon_H72 zenon_H65 zenon_H66 zenon_H49 zenon_H2ce zenon_H33a zenon_H7c zenon_H125 zenon_Hf8 zenon_H33 zenon_H46 zenon_H45 zenon_H3d zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H2d1 zenon_H8c zenon_H2e0 zenon_H10e zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hcf zenon_Haf zenon_Hcb zenon_Hde zenon_Hd3 zenon_Hda zenon_H24 zenon_H23 zenon_H2c9 zenon_Hb0 zenon_H2db zenon_H2c5 zenon_H2e1 zenon_H95 zenon_H9e zenon_H4b zenon_Hb5 zenon_H341 zenon_H54 zenon_H19. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.50 apply (zenon_L74_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.50 apply (zenon_L492_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.50 apply (zenon_L493_); trivial. % 51.29/51.50 apply (zenon_L33_); trivial. % 51.29/51.50 (* end of lemma zenon_L494_ *) % 51.29/51.50 assert (zenon_L495_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e22)) = (e21)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.50 do 0 intro. intros zenon_Hf8 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hcf zenon_Hb0 zenon_H9e zenon_H95 zenon_Hab zenon_Haf zenon_H4b zenon_Hb5 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hcb zenon_H3d zenon_H128 zenon_H108 zenon_H345 zenon_H15e zenon_H349 zenon_H14 zenon_H13 zenon_H14e zenon_H293 zenon_H2e7 zenon_H34c zenon_H126 zenon_H8c zenon_H2d1 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H46 zenon_H2c6 zenon_H1c zenon_H7c zenon_H2c zenon_H33a zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H305 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hec zenon_H19. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.50 apply (zenon_L328_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.50 apply (zenon_L299_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.50 apply (zenon_L489_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H11a | zenon_intro zenon_H346 ]. % 51.29/51.50 apply (zenon_L488_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H346); [ zenon_intro zenon_H129 | zenon_intro zenon_H347 ]. % 51.29/51.50 apply (zenon_L359_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H335 | zenon_intro zenon_Hed ]. % 51.29/51.50 apply (zenon_L475_); trivial. % 51.29/51.50 apply (zenon_L63_); trivial. % 51.29/51.50 (* end of lemma zenon_L495_ *) % 51.29/51.50 assert (zenon_L496_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H33e zenon_H10b zenon_H2c9 zenon_H66 zenon_H126 zenon_H8c zenon_H1c zenon_Hc2 zenon_H327 zenon_H2d1 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hb0 zenon_Hda zenon_H49 zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H35 zenon_H42 zenon_Hd3 zenon_H65 zenon_Hde zenon_H3d zenon_H9e zenon_H19. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.29/51.50 apply (zenon_L75_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.29/51.50 apply (zenon_L282_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.29/51.50 apply (zenon_L454_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.29/51.50 apply (zenon_L334_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.50 apply (zenon_L39_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.50 apply (zenon_L439_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.50 apply (zenon_L41_); trivial. % 51.29/51.50 apply (zenon_L24_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.29/51.50 apply (zenon_L451_); trivial. % 51.29/51.50 apply (zenon_L452_); trivial. % 51.29/51.50 (* end of lemma zenon_L496_ *) % 51.29/51.50 assert (zenon_L497_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H341 zenon_H23 zenon_H2db zenon_H105 zenon_H125 zenon_H24 zenon_H2c5 zenon_Hff zenon_H9e zenon_H3d zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H42 zenon_Hda zenon_Hd3 zenon_He1 zenon_H54 zenon_H65 zenon_Hde zenon_H31e zenon_H2be zenon_H72 zenon_H2ce zenon_H33a zenon_H46 zenon_H2d1 zenon_H66 zenon_H2c9 zenon_H10b zenon_H33e zenon_H345 zenon_H327 zenon_H126 zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H49 zenon_H7c zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H2c zenon_H1c zenon_Hab. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.50 apply (zenon_L325_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.50 apply (zenon_L496_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.50 apply (zenon_L13_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.50 apply (zenon_L471_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.29/51.50 apply (zenon_L75_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.29/51.50 apply (zenon_L491_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.29/51.50 apply (zenon_L477_); trivial. % 51.29/51.50 apply (zenon_L452_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.50 apply (zenon_L333_); trivial. % 51.29/51.50 apply (zenon_L34_); trivial. % 51.29/51.50 (* end of lemma zenon_L497_ *) % 51.29/51.50 assert (zenon_L498_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e20) (e22)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (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))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H13b zenon_H34c zenon_H2e7 zenon_H293 zenon_H14e zenon_H13 zenon_H14 zenon_H349 zenon_H15e zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H2ce zenon_H2e0 zenon_H318 zenon_H327 zenon_H32a zenon_H31b zenon_H2be zenon_H31e zenon_H341 zenon_H2c5 zenon_H33a zenon_H2d1 zenon_H2c9 zenon_H33e zenon_H345 zenon_H2d4 zenon_H314 zenon_H30d zenon_H311 zenon_H305 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.29/51.50 apply (zenon_L7_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.29/51.50 apply (zenon_L281_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.29/51.50 apply (zenon_L282_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.29/51.50 apply (zenon_L7_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.29/51.50 apply (zenon_L325_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.50 apply (zenon_L11_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.50 apply (zenon_L11_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.50 apply (zenon_L12_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.50 apply (zenon_L283_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.50 apply (zenon_L328_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.50 apply (zenon_L455_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.50 apply (zenon_L359_); trivial. % 51.29/51.50 apply (zenon_L33_); trivial. % 51.29/51.50 apply (zenon_L369_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.50 apply (zenon_L486_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.50 apply (zenon_L283_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.50 apply (zenon_L99_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.50 apply (zenon_L328_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.50 apply (zenon_L299_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.50 apply (zenon_L489_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H345); [ zenon_intro zenon_H11a | zenon_intro zenon_H346 ]. % 51.29/51.50 apply (zenon_L488_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H346); [ zenon_intro zenon_H129 | zenon_intro zenon_H347 ]. % 51.29/51.50 apply (zenon_L359_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H347); [ zenon_intro zenon_H335 | zenon_intro zenon_Hed ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.50 apply (zenon_L39_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.50 apply (zenon_L490_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.50 apply (zenon_L41_); trivial. % 51.29/51.50 apply (zenon_L24_); trivial. % 51.29/51.50 apply (zenon_L63_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.50 apply (zenon_L454_); trivial. % 51.29/51.50 apply (zenon_L34_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.50 apply (zenon_L479_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.50 apply (zenon_L359_); trivial. % 51.29/51.50 apply (zenon_L33_); trivial. % 51.29/51.50 apply (zenon_L377_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.50 apply (zenon_L494_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.50 apply (zenon_L283_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.29/51.50 apply (zenon_L99_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.29/51.50 apply (zenon_L495_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.29/51.50 apply (zenon_L333_); trivial. % 51.29/51.50 apply (zenon_L34_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.50 apply (zenon_L497_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.50 apply (zenon_L359_); trivial. % 51.29/51.50 apply (zenon_L33_); trivial. % 51.29/51.50 apply (zenon_L377_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.50 apply (zenon_L378_); trivial. % 51.29/51.50 apply (zenon_L335_); trivial. % 51.29/51.50 apply (zenon_L384_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.29/51.50 apply (zenon_L426_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.29/51.50 apply (zenon_L488_); trivial. % 51.29/51.50 apply (zenon_L85_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.29/51.50 apply (zenon_L4_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.29/51.50 apply (zenon_L109_); trivial. % 51.29/51.50 apply (zenon_L47_); trivial. % 51.29/51.50 (* end of lemma zenon_L498_ *) % 51.29/51.50 assert (zenon_L499_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H32a zenon_H2b zenon_H2ba zenon_H1c zenon_H2c zenon_H2be zenon_H357 zenon_H349 zenon_H2ea zenon_H13. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.29/51.50 apply (zenon_L7_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.29/51.50 apply (zenon_L281_); trivial. % 51.29/51.50 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.29/51.50 apply (zenon_L282_); trivial. % 51.29/51.50 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))). % 51.29/51.50 intro zenon_D_pnotp. % 51.29/51.50 apply zenon_H357. % 51.29/51.50 rewrite <- zenon_D_pnotp. % 51.29/51.50 exact zenon_H349. % 51.29/51.50 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H358]. % 51.29/51.50 cut (((h4 (e12)) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H359]. % 51.29/51.50 congruence. % 51.29/51.50 elim (classic ((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [ zenon_intro zenon_H35a | zenon_intro zenon_H35b ]. % 51.29/51.50 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13)))) = ((h4 (e12)) = (h4 (op1 (e10) (e13))))). % 51.29/51.50 intro zenon_D_pnotp. % 51.29/51.50 apply zenon_H359. % 51.29/51.50 rewrite <- zenon_D_pnotp. % 51.29/51.50 exact zenon_H35a. % 51.29/51.50 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H35b]. % 51.29/51.50 cut (((h4 (op1 (e10) (e13))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H35c]. % 51.29/51.50 congruence. % 51.29/51.50 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 51.29/51.50 congruence. % 51.29/51.50 exact (zenon_H4f zenon_H49). % 51.29/51.50 apply zenon_H35b. apply refl_equal. % 51.29/51.50 apply zenon_H35b. apply refl_equal. % 51.29/51.50 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H35d]. % 51.29/51.50 cut (((op2 (e23) (op2 (e23) (e23))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H35e]. % 51.29/51.50 congruence. % 51.29/51.50 apply zenon_H35e. apply sym_equal. exact zenon_H13. % 51.29/51.50 apply zenon_H35d. apply sym_equal. exact zenon_H2ea. % 51.29/51.50 (* end of lemma zenon_L499_ *) % 51.29/51.50 assert (zenon_L500_ : (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> ((op1 (e11) (e10)) = (e11)) -> ((op2 (e21) (e20)) = (e21)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.29/51.50 do 0 intro. intros zenon_H35f zenon_H108 zenon_H280 zenon_H2e7 zenon_H14e zenon_H13 zenon_H14. % 51.29/51.50 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))). % 51.29/51.50 intro zenon_D_pnotp. % 51.29/51.50 apply zenon_H35f. % 51.29/51.50 rewrite <- zenon_D_pnotp. % 51.29/51.50 exact zenon_H2e7. % 51.29/51.50 cut (((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H360]. % 51.29/51.50 cut (((h4 (e11)) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H361]. % 51.29/51.50 congruence. % 51.29/51.50 elim (classic ((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [ zenon_intro zenon_H362 | zenon_intro zenon_H363 ]. % 51.29/51.50 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10)))) = ((h4 (e11)) = (h4 (op1 (e11) (e10))))). % 51.29/51.50 intro zenon_D_pnotp. % 51.29/51.50 apply zenon_H361. % 51.29/51.50 rewrite <- zenon_D_pnotp. % 51.29/51.50 exact zenon_H362. % 51.29/51.50 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H363]. % 51.29/51.50 cut (((h4 (op1 (e11) (e10))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H364]. % 51.29/51.50 congruence. % 51.29/51.50 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 51.29/51.50 congruence. % 51.29/51.50 exact (zenon_H109 zenon_H108). % 51.29/51.50 apply zenon_H363. apply refl_equal. % 51.29/51.50 apply zenon_H363. apply refl_equal. % 51.29/51.50 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H365 | zenon_intro zenon_H366 ]. % 51.29/51.50 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))). % 51.29/51.50 intro zenon_D_pnotp. % 51.29/51.50 apply zenon_H360. % 51.29/51.50 rewrite <- zenon_D_pnotp. % 51.29/51.50 exact zenon_H365. % 51.29/51.50 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H366]. % 51.29/51.50 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 51.29/51.50 congruence. % 51.29/51.50 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))). % 51.29/51.50 intro zenon_D_pnotp. % 51.29/51.50 apply zenon_H367. % 51.29/51.50 rewrite <- zenon_D_pnotp. % 51.29/51.50 exact zenon_H280. % 51.29/51.50 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 51.29/51.50 cut (((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H368]. % 51.29/51.50 congruence. % 51.29/51.50 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H365 | zenon_intro zenon_H366 ]. % 51.29/51.50 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))). % 51.29/51.50 intro zenon_D_pnotp. % 51.29/51.50 apply zenon_H368. % 51.29/51.50 rewrite <- zenon_D_pnotp. % 51.29/51.50 exact zenon_H365. % 51.29/51.50 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H366]. % 51.29/51.50 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H369]. % 51.29/51.50 congruence. % 51.29/51.50 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 51.29/51.50 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 51.29/51.50 congruence. % 51.29/51.50 apply (zenon_L326_); trivial. % 51.29/51.50 apply (zenon_L1_); trivial. % 51.29/51.50 apply zenon_H366. apply refl_equal. % 51.29/51.50 apply zenon_H366. apply refl_equal. % 51.29/51.50 exact (zenon_H243 zenon_H14e). % 51.29/51.50 apply zenon_H366. apply refl_equal. % 51.29/51.50 apply zenon_H366. apply refl_equal. % 51.29/51.50 (* end of lemma zenon_L500_ *) % 51.29/51.50 assert (zenon_L501_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.50 do 0 intro. intros zenon_Hab zenon_H1c zenon_H2c zenon_H126 zenon_H35 zenon_H33e zenon_H10b zenon_H2c9 zenon_H2e1 zenon_H8c zenon_Hc2 zenon_H327 zenon_H2d1 zenon_H46 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hb0 zenon_Hda zenon_H49 zenon_Hea zenon_H41 zenon_He1 zenon_Haf zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H42 zenon_Hd3 zenon_H65 zenon_Hde zenon_H3d zenon_H9e zenon_Hff zenon_H2c5 zenon_H24 zenon_H105 zenon_H2db zenon_H23 zenon_H341 zenon_H11a zenon_H125 zenon_H54 zenon_H19. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.51 apply (zenon_L328_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.51 apply (zenon_L455_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.51 apply (zenon_L482_); trivial. % 51.29/51.51 apply (zenon_L33_); trivial. % 51.29/51.51 (* end of lemma zenon_L501_ *) % 51.29/51.51 assert (zenon_L502_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H54 zenon_H125 zenon_H11a zenon_H341 zenon_H23 zenon_H2db zenon_H24 zenon_H2c5 zenon_Hff zenon_H90 zenon_H318 zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H314 zenon_Hfb zenon_Hf6 zenon_H2e0 zenon_H7d zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H113 zenon_H31b zenon_Haf zenon_H41 zenon_Hb0 zenon_H72 zenon_H2ce zenon_H33a zenon_H46 zenon_H2d1 zenon_H327 zenon_H2c9 zenon_H10b zenon_H33e zenon_Hf8 zenon_H49 zenon_Hea zenon_He1 zenon_H7c zenon_H305 zenon_H2e1 zenon_H2ff zenon_H35 zenon_H2be zenon_H31e zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H42. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.51 apply (zenon_L12_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.51 apply (zenon_L283_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.51 apply (zenon_L501_); trivial. % 51.29/51.51 apply (zenon_L377_); trivial. % 51.29/51.51 (* end of lemma zenon_L502_ *) % 51.29/51.51 assert (zenon_L503_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.51 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H3d zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_Hde zenon_Hd3 zenon_Hda zenon_H90 zenon_H35 zenon_H49 zenon_H42 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_H19 zenon_H8c. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.51 apply (zenon_L86_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.51 apply (zenon_L13_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.51 apply (zenon_L47_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.51 apply (zenon_L314_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.51 apply (zenon_L290_); trivial. % 51.29/51.51 apply (zenon_L24_); trivial. % 51.29/51.51 apply (zenon_L301_); trivial. % 51.29/51.51 (* end of lemma zenon_L503_ *) % 51.29/51.51 assert (zenon_L504_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H11a zenon_H2c9 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H42 zenon_H49 zenon_H90 zenon_Hda zenon_Hd3 zenon_Hde zenon_H45 zenon_H46 zenon_H34 zenon_Hf8 zenon_H3d zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H95 zenon_Hab zenon_H2c zenon_Haf zenon_H4b zenon_Hb5 zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.29/51.51 apply (zenon_L281_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.29/51.51 apply (zenon_L284_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.29/51.51 apply (zenon_L503_); trivial. % 51.29/51.51 apply (zenon_L309_); trivial. % 51.29/51.51 (* end of lemma zenon_L504_ *) % 51.29/51.51 assert (zenon_L505_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.51 do 0 intro. intros zenon_Hcf zenon_H35 zenon_Hb5 zenon_H4b zenon_Haf zenon_H2c zenon_Hab zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_Hde zenon_Hd3 zenon_Hda zenon_H90 zenon_H49 zenon_H72 zenon_H65 zenon_H54 zenon_H2c9 zenon_H11a zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.51 apply (zenon_L504_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.51 apply (zenon_L42_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.51 apply (zenon_L43_); trivial. % 51.29/51.51 apply (zenon_L37_); trivial. % 51.29/51.51 (* end of lemma zenon_L505_ *) % 51.29/51.51 assert (zenon_L506_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.51 do 0 intro. intros zenon_Hcf zenon_H72 zenon_H65 zenon_H62 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_H42 zenon_Hbe zenon_H8c zenon_H1c zenon_Hc2 zenon_He1 zenon_H54 zenon_H51 zenon_H10a zenon_H10e zenon_H49 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H3d zenon_H19. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.51 apply (zenon_L289_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.51 apply (zenon_L40_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.51 apply (zenon_L344_); trivial. % 51.29/51.51 apply (zenon_L37_); trivial. % 51.29/51.51 (* end of lemma zenon_L506_ *) % 51.29/51.51 assert (zenon_L507_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H90 zenon_H35 zenon_H3d zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H49 zenon_H10e zenon_H10a zenon_H51 zenon_H54 zenon_He1 zenon_Hc2 zenon_H1c zenon_Hbe zenon_H42 zenon_H2c8 zenon_H11a zenon_H2c9 zenon_H65 zenon_H72 zenon_Hcf zenon_H19 zenon_H8c. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.29/51.51 apply (zenon_L16_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.29/51.51 apply (zenon_L17_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.29/51.51 apply (zenon_L506_); trivial. % 51.29/51.51 apply (zenon_L24_); trivial. % 51.29/51.51 (* end of lemma zenon_L507_ *) % 51.29/51.51 assert (zenon_L508_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.51 do 0 intro. intros zenon_Hcf zenon_H72 zenon_H65 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_H42 zenon_He1 zenon_H54 zenon_H51 zenon_H10a zenon_H10e zenon_H49 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H3d zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.51 apply (zenon_L39_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.51 apply (zenon_L507_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.51 apply (zenon_L41_); trivial. % 51.29/51.51 apply (zenon_L24_); trivial. % 51.29/51.51 (* end of lemma zenon_L508_ *) % 51.29/51.51 assert (zenon_L509_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.29/51.51 do 0 intro. intros zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_Hda zenon_H49 zenon_H10e zenon_H10a zenon_Hbe zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_H19. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.29/51.51 apply (zenon_L57_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.29/51.51 apply (zenon_L40_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.29/51.51 apply (zenon_L77_); trivial. % 51.29/51.51 apply (zenon_L37_); trivial. % 51.29/51.51 (* end of lemma zenon_L509_ *) % 51.29/51.51 assert (zenon_L510_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.29/51.51 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_H10a zenon_H10e zenon_H49 zenon_Hda zenon_H42 zenon_He8 zenon_H4b zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.29/51.51 apply (zenon_L39_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.29/51.51 apply (zenon_L509_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.29/51.51 apply (zenon_L41_); trivial. % 51.29/51.51 apply (zenon_L24_); trivial. % 51.29/51.51 (* end of lemma zenon_L510_ *) % 51.29/51.51 assert (zenon_L511_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e10) = (e12))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.29/51.51 do 0 intro. intros zenon_Hfe zenon_H2b zenon_H90 zenon_H2c9 zenon_H65 zenon_H72 zenon_Haf zenon_Ha2 zenon_Hde zenon_Hd3 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H35 zenon_H10b zenon_Hff zenon_H23 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hcf zenon_H42 zenon_Hda zenon_H10e zenon_H10a zenon_H54 zenon_He1 zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb0 zenon_Hea zenon_Hab zenon_H2c zenon_H95 zenon_H9e zenon_Hb5 zenon_Hf8 zenon_H3d zenon_H11a zenon_H49 zenon_H4b. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.29/51.51 apply (zenon_L7_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.51 apply (zenon_L317_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.29/51.51 apply (zenon_L281_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.29/51.51 apply (zenon_L284_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.51 apply (zenon_L86_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.51 apply (zenon_L13_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.51 apply (zenon_L505_); trivial. % 51.29/51.51 apply (zenon_L508_); trivial. % 51.29/51.51 apply (zenon_L309_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.51 apply (zenon_L427_); trivial. % 51.29/51.51 apply (zenon_L15_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.29/51.51 apply (zenon_L75_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.51 apply (zenon_L317_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.29/51.51 apply (zenon_L354_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.29/51.51 apply (zenon_L13_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.29/51.51 apply (zenon_L65_); trivial. % 51.29/51.51 apply (zenon_L510_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.51 apply (zenon_L427_); trivial. % 51.29/51.51 apply (zenon_L15_); trivial. % 51.29/51.51 (* end of lemma zenon_L511_ *) % 51.29/51.51 assert (zenon_L512_ : (~((e12) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e11) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e11) = (e12))) -> (~((e10) = (e12))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((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)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H4b zenon_H11a zenon_H3d zenon_Hf8 zenon_Hb5 zenon_H9e zenon_H95 zenon_Hea zenon_Hb0 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_He1 zenon_H54 zenon_H10a zenon_H10e zenon_H42 zenon_Hcf zenon_Hc2 zenon_H19 zenon_H8c zenon_H23 zenon_Hff zenon_H10b zenon_H35 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_Hde zenon_Ha2 zenon_Haf zenon_H72 zenon_H65 zenon_H2c9 zenon_H90 zenon_H2b zenon_Hfe zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.29/51.51 apply (zenon_L511_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.29/51.51 apply (zenon_L34_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.29/51.51 apply (zenon_L45_); trivial. % 51.29/51.51 apply (zenon_L46_); trivial. % 51.29/51.51 (* end of lemma zenon_L512_ *) % 51.29/51.51 assert (zenon_L513_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((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))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H13b zenon_H318 zenon_H2db zenon_H305 zenon_H311 zenon_H2ff zenon_H30d zenon_H314 zenon_H2e0 zenon_H2ce zenon_H2d4 zenon_H327 zenon_H345 zenon_H33e zenon_H2d1 zenon_H33a zenon_H341 zenon_H31e zenon_H2be zenon_H31b zenon_H32a zenon_H14 zenon_H13 zenon_H14e zenon_H2e7 zenon_H280 zenon_H35f zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.29/51.51 apply (zenon_L7_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.29/51.51 apply (zenon_L281_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.29/51.51 apply (zenon_L282_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.29/51.51 apply (zenon_L7_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.29/51.51 apply (zenon_L325_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.51 apply (zenon_L317_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.51 apply (zenon_L317_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.51 apply (zenon_L12_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.51 apply (zenon_L283_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.51 apply (zenon_L500_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.51 apply (zenon_L455_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.51 apply (zenon_L359_); trivial. % 51.29/51.51 apply (zenon_L33_); trivial. % 51.29/51.51 apply (zenon_L369_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.51 apply (zenon_L486_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.51 apply (zenon_L283_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.51 apply (zenon_L500_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.51 apply (zenon_L479_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.51 apply (zenon_L359_); trivial. % 51.29/51.51 apply (zenon_L33_); trivial. % 51.29/51.51 apply (zenon_L377_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.51 apply (zenon_L494_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.51 apply (zenon_L283_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.51 apply (zenon_L500_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.51 apply (zenon_L497_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.51 apply (zenon_L359_); trivial. % 51.29/51.51 apply (zenon_L33_); trivial. % 51.29/51.51 apply (zenon_L377_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.51 apply (zenon_L378_); trivial. % 51.29/51.51 apply (zenon_L15_); trivial. % 51.29/51.51 apply (zenon_L384_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.29/51.51 apply (zenon_L426_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.29/51.51 apply (zenon_L7_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.29/51.51 apply (zenon_L281_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.29/51.51 apply (zenon_L282_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.29/51.51 apply (zenon_L7_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.29/51.51 apply (zenon_L325_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.29/51.51 apply (zenon_L11_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.29/51.51 apply (zenon_L11_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.29/51.51 apply (zenon_L502_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.51 apply (zenon_L500_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.51 apply (zenon_L479_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.51 apply (zenon_L482_); trivial. % 51.29/51.51 apply (zenon_L33_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.29/51.51 apply (zenon_L494_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.29/51.51 apply (zenon_L283_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.29/51.51 apply (zenon_L500_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.29/51.51 apply (zenon_L497_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.29/51.51 apply (zenon_L482_); trivial. % 51.29/51.51 apply (zenon_L33_); trivial. % 51.29/51.51 apply (zenon_L377_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.29/51.51 apply (zenon_L378_); trivial. % 51.29/51.51 apply (zenon_L335_); trivial. % 51.29/51.51 apply (zenon_L384_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.29/51.51 apply (zenon_L500_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.29/51.51 apply (zenon_L512_); trivial. % 51.29/51.51 apply (zenon_L82_); trivial. % 51.29/51.51 apply (zenon_L85_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.29/51.51 apply (zenon_L4_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.29/51.51 apply (zenon_L109_); trivial. % 51.29/51.51 apply (zenon_L47_); trivial. % 51.29/51.51 (* end of lemma zenon_L513_ *) % 51.29/51.51 assert (zenon_L514_ : (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((op2 (e21) (e20)) = (e22)) -> ((op2 (e21) (e21)) = (e22)) -> False). % 51.29/51.51 do 0 intro. intros zenon_H36a zenon_H16e zenon_H17c. % 51.29/51.51 cut (((op2 (e21) (e20)) = (e22)) = ((op2 (e21) (e20)) = (op2 (e21) (e21)))). % 51.29/51.51 intro zenon_D_pnotp. % 51.29/51.51 apply zenon_H36a. % 51.29/51.51 rewrite <- zenon_D_pnotp. % 51.29/51.51 exact zenon_H16e. % 51.29/51.51 cut (((e22) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 51.29/51.51 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 51.29/51.51 congruence. % 51.29/51.51 apply zenon_H1aa. apply refl_equal. % 51.29/51.51 apply zenon_H17d. apply sym_equal. exact zenon_H17c. % 51.29/51.51 (* end of lemma zenon_L514_ *) % 51.29/51.51 assert (zenon_L515_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H1fa zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H1ac zenon_H19b zenon_H205 zenon_H1a8 zenon_H252 zenon_H254 zenon_H1f7 zenon_H14e. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.29/51.51 apply (zenon_L194_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.29/51.51 apply (zenon_L184_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.29/51.51 apply (zenon_L189_); trivial. % 51.29/51.51 apply (zenon_L149_); trivial. % 51.29/51.51 (* end of lemma zenon_L515_ *) % 51.29/51.51 assert (zenon_L516_ : (~((op2 (e21) (e21)) = (op2 (op2 (e20) (e22)) (op2 (e20) (e22))))) -> ((op2 (e20) (e22)) = (e21)) -> False). % 51.29/51.51 do 0 intro. intros zenon_H36b zenon_H293. % 51.29/51.51 cut (((e21) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H36c]. % 51.29/51.51 cut (((e21) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H36c]. % 51.29/51.51 congruence. % 51.29/51.51 apply zenon_H36c. apply sym_equal. exact zenon_H293. % 51.29/51.51 apply zenon_H36c. apply sym_equal. exact zenon_H293. % 51.29/51.51 (* end of lemma zenon_L516_ *) % 51.29/51.51 assert (zenon_L517_ : ((op2 (e22) (e21)) = (e22)) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H226 zenon_H293 zenon_H36d zenon_H1bd zenon_H1bc zenon_H1cd zenon_H1c9 zenon_H1cc zenon_H14e zenon_H244 zenon_H245. % 51.29/51.51 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.29/51.51 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_H1b3. zenon_intro zenon_H1b2. % 51.29/51.51 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b5. zenon_intro zenon_H1b4. % 51.29/51.51 apply (zenon_and_s _ _ zenon_H1b4). zenon_intro zenon_H1b7. zenon_intro zenon_H1b6. % 51.29/51.51 cut (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (e22)) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))). % 51.29/51.51 intro zenon_D_pnotp. % 51.29/51.51 apply zenon_H36d. % 51.29/51.51 rewrite <- zenon_D_pnotp. % 51.29/51.51 exact zenon_H1b7. % 51.29/51.51 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 51.29/51.51 cut (((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H36e]. % 51.29/51.51 congruence. % 51.29/51.51 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H246 | zenon_intro zenon_H247 ]. % 51.29/51.51 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e20) (e22)) (op2 (e20) (e22))) = (op2 (e21) (e21)))). % 51.29/51.51 intro zenon_D_pnotp. % 51.29/51.51 apply zenon_H36e. % 51.29/51.51 rewrite <- zenon_D_pnotp. % 51.29/51.51 exact zenon_H246. % 51.29/51.51 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 51.29/51.51 cut (((op2 (e21) (e21)) = (op2 (op2 (e20) (e22)) (op2 (e20) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H36b]. % 51.29/51.51 congruence. % 51.29/51.51 apply (zenon_L516_); trivial. % 51.29/51.51 apply zenon_H247. apply refl_equal. % 51.29/51.51 apply zenon_H247. apply refl_equal. % 51.29/51.51 apply zenon_H227. apply sym_equal. exact zenon_H226. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.29/51.51 apply (zenon_L134_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.29/51.51 apply (zenon_L136_); trivial. % 51.29/51.51 apply (zenon_L172_); trivial. % 51.29/51.51 (* end of lemma zenon_L517_ *) % 51.29/51.51 assert (zenon_L518_ : (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (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 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H245 zenon_H244 zenon_H14e zenon_H1e7 zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H19b zenon_H1cc zenon_H1cd zenon_H1f3 zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.29/51.51 apply (zenon_L179_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.29/51.51 apply (zenon_L124_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.29/51.51 apply (zenon_L125_); trivial. % 51.29/51.51 apply (zenon_L126_); trivial. % 51.29/51.51 (* end of lemma zenon_L518_ *) % 51.29/51.51 assert (zenon_L519_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H175 zenon_H1c9 zenon_H36d zenon_H293 zenon_H226 zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H1f3 zenon_H1cd zenon_H1cc zenon_H19b zenon_H1e6 zenon_H1bd zenon_H1ec zenon_H244 zenon_H245 zenon_H1f7 zenon_H14e. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.29/51.51 apply (zenon_L132_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.29/51.51 apply (zenon_L517_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.29/51.51 apply (zenon_L518_); trivial. % 51.29/51.51 apply (zenon_L149_); trivial. % 51.29/51.51 (* end of lemma zenon_L519_ *) % 51.29/51.51 assert (zenon_L520_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H19b zenon_H245 zenon_H244 zenon_H14e zenon_H1b1 zenon_H1c9 zenon_H252 zenon_H1bc zenon_H1bd zenon_H1d7 zenon_H21b zenon_H21c zenon_H23c zenon_H209 zenon_H24b zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.29/51.51 apply (zenon_L187_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.29/51.51 apply (zenon_L124_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.29/51.51 apply (zenon_L125_); trivial. % 51.29/51.51 apply (zenon_L126_); trivial. % 51.29/51.51 (* end of lemma zenon_L520_ *) % 51.29/51.51 assert (zenon_L521_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 51.29/51.51 do 0 intro. intros zenon_H1fd zenon_H1cd zenon_H204. % 51.29/51.51 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))). % 51.29/51.51 intro zenon_D_pnotp. % 51.29/51.51 apply zenon_H1fd. % 51.29/51.51 rewrite <- zenon_D_pnotp. % 51.29/51.51 exact zenon_H1cd. % 51.29/51.51 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H36f]. % 51.29/51.51 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 51.29/51.51 congruence. % 51.29/51.51 apply zenon_H201. apply refl_equal. % 51.29/51.51 apply zenon_H36f. apply sym_equal. exact zenon_H204. % 51.29/51.51 (* end of lemma zenon_L521_ *) % 51.29/51.51 assert (zenon_L522_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e23)) -> False). % 51.29/51.51 do 0 intro. intros zenon_H21f zenon_H217 zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H24b zenon_H209 zenon_H23c zenon_H21b zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H252 zenon_H1c9 zenon_H1b1 zenon_H14e zenon_H244 zenon_H245 zenon_H19b zenon_H1fd zenon_H204. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H220 ]. % 51.29/51.51 apply (zenon_L151_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H218 | zenon_intro zenon_H221 ]. % 51.29/51.51 apply (zenon_L156_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H21c | zenon_intro zenon_H1cd ]. % 51.29/51.51 apply (zenon_L520_); trivial. % 51.29/51.51 apply (zenon_L521_); trivial. % 51.29/51.51 (* end of lemma zenon_L522_ *) % 51.29/51.51 assert (zenon_L523_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H204 zenon_H1b1 zenon_H1c9 zenon_H252 zenon_H1d7 zenon_H23c zenon_H209 zenon_H24b zenon_H245 zenon_H244 zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H175 zenon_H15e zenon_H14 zenon_H187 zenon_H19b zenon_H1cc zenon_H18e zenon_H195 zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H1fd zenon_H21f zenon_H1f7 zenon_H14e. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.29/51.51 apply (zenon_L132_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.29/51.51 apply (zenon_L522_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.29/51.51 apply (zenon_L180_); trivial. % 51.29/51.51 apply (zenon_L149_); trivial. % 51.29/51.51 (* end of lemma zenon_L523_ *) % 51.29/51.51 assert (zenon_L524_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H22f zenon_H16f zenon_H205 zenon_H245 zenon_H244 zenon_H1b1 zenon_H252 zenon_H1bc zenon_H1bd zenon_H1d7 zenon_H175 zenon_H21d zenon_H14e zenon_H210. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.29/51.51 apply (zenon_L129_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.29/51.51 apply (zenon_L184_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.29/51.51 apply (zenon_L186_); trivial. % 51.29/51.51 apply (zenon_L154_); trivial. % 51.29/51.51 (* end of lemma zenon_L524_ *) % 51.29/51.51 assert (zenon_L525_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e21))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.29/51.51 do 0 intro. intros zenon_H1fa zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H1ac zenon_H19b zenon_H210 zenon_H21d zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H244 zenon_H245 zenon_H205 zenon_H16f zenon_H22f zenon_H252 zenon_H254 zenon_H1f7 zenon_H14e. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.29/51.51 apply (zenon_L194_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.29/51.51 apply (zenon_L524_); trivial. % 51.29/51.51 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.29/51.51 apply (zenon_L189_); trivial. % 51.29/51.51 apply (zenon_L149_); trivial. % 51.29/51.51 (* end of lemma zenon_L525_ *) % 51.29/51.51 assert (zenon_L526_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e23)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e21))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H222 zenon_H226 zenon_H293 zenon_H36d zenon_H21f zenon_H1fd zenon_H217 zenon_H1d8 zenon_H21b zenon_H1f3 zenon_H1cc zenon_H1e6 zenon_H1ec zenon_H24b zenon_H209 zenon_H23c zenon_H1c9 zenon_H254 zenon_H252 zenon_H22f zenon_H16f zenon_H205 zenon_H245 zenon_H244 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H175 zenon_H210 zenon_H19b zenon_H1ac zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195 zenon_H1fa zenon_H1f7 zenon_H14e. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.35/51.51 apply (zenon_L519_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.35/51.51 apply (zenon_L523_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.35/51.51 apply (zenon_L525_); trivial. % 51.35/51.51 apply (zenon_L149_); trivial. % 51.35/51.51 (* end of lemma zenon_L526_ *) % 51.35/51.51 assert (zenon_L527_ : (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e22) (e21)) = (e22)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H1f7 zenon_H1fa zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H1ac zenon_H19b zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H244 zenon_H245 zenon_H205 zenon_H16f zenon_H22f zenon_H252 zenon_H254 zenon_H23c zenon_H209 zenon_H24b zenon_H1ec zenon_H1e6 zenon_H1cc zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H1fd zenon_H21f zenon_H36d zenon_H293 zenon_H226 zenon_H222 zenon_H14e zenon_H210. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.35/51.51 apply (zenon_L183_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.35/51.51 apply (zenon_L515_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.35/51.51 apply (zenon_L526_); trivial. % 51.35/51.51 apply (zenon_L154_); trivial. % 51.35/51.51 (* end of lemma zenon_L527_ *) % 51.35/51.51 assert (zenon_L528_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e22) (e21)) = (e22)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H24e zenon_H203 zenon_H18e zenon_H187 zenon_H1f7 zenon_H1fa zenon_H1ac zenon_H19b zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H244 zenon_H245 zenon_H205 zenon_H16f zenon_H22f zenon_H252 zenon_H254 zenon_H23c zenon_H209 zenon_H24b zenon_H1ec zenon_H1e6 zenon_H1cc zenon_H1f3 zenon_H21b zenon_H217 zenon_H1fd zenon_H21f zenon_H36d zenon_H293 zenon_H226 zenon_H222 zenon_H14e zenon_H210 zenon_H15e zenon_H14 zenon_H195. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.35/51.51 apply (zenon_L191_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.35/51.51 apply (zenon_L162_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.35/51.51 apply (zenon_L527_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.35/51.51 apply (zenon_L124_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.35/51.51 apply (zenon_L125_); trivial. % 51.35/51.51 apply (zenon_L126_); trivial. % 51.35/51.51 apply (zenon_L126_); trivial. % 51.35/51.51 (* end of lemma zenon_L528_ *) % 51.35/51.51 assert (zenon_L529_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e23)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H214 zenon_H195 zenon_H15e zenon_H222 zenon_H226 zenon_H293 zenon_H36d zenon_H21f zenon_H1fd zenon_H217 zenon_H21b zenon_H1f3 zenon_H1cc zenon_H1e6 zenon_H1ec zenon_H24b zenon_H23c zenon_H254 zenon_H252 zenon_H22f zenon_H16f zenon_H205 zenon_H245 zenon_H244 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H19b zenon_H1ac zenon_H1fa zenon_H1f7 zenon_H187 zenon_H18e zenon_H24e zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.35/51.51 apply (zenon_L151_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.35/51.51 apply (zenon_L528_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.35/51.51 apply (zenon_L153_); trivial. % 51.35/51.51 apply (zenon_L154_); trivial. % 51.35/51.51 (* end of lemma zenon_L529_ *) % 51.35/51.51 assert (zenon_L530_ : (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((op2 (e21) (e20)) = (e22)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e22)) = (e21)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H22b zenon_H164 zenon_H16e zenon_H36a zenon_H24e zenon_H18e zenon_H187 zenon_H1f7 zenon_H1fa zenon_H1ac zenon_H19b zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H244 zenon_H245 zenon_H205 zenon_H22f zenon_H252 zenon_H254 zenon_H23c zenon_H24b zenon_H1ec zenon_H1e6 zenon_H1cc zenon_H1f3 zenon_H21b zenon_H217 zenon_H21f zenon_H36d zenon_H293 zenon_H222 zenon_H15e zenon_H195 zenon_H214 zenon_H1fd zenon_H16f zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H165 | zenon_intro zenon_H22c ]. % 51.35/51.51 apply (zenon_L117_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H17c | zenon_intro zenon_H22d ]. % 51.35/51.51 apply (zenon_L514_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H226 | zenon_intro zenon_H229 ]. % 51.35/51.51 apply (zenon_L529_); trivial. % 51.35/51.51 apply (zenon_L163_); trivial. % 51.35/51.51 (* end of lemma zenon_L530_ *) % 51.35/51.51 assert (zenon_L531_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (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 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H22f zenon_H16f zenon_H205 zenon_H1f7 zenon_H245 zenon_H244 zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H19b zenon_H1cc zenon_H1cd zenon_H1f3 zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195 zenon_H226 zenon_H293 zenon_H36d zenon_H175 zenon_H1ac zenon_H1fa zenon_H14e zenon_H210. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.35/51.51 apply (zenon_L183_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.35/51.51 apply (zenon_L243_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.35/51.51 apply (zenon_L519_); trivial. % 51.35/51.51 apply (zenon_L154_); trivial. % 51.35/51.51 (* end of lemma zenon_L531_ *) % 51.35/51.51 assert (zenon_L532_ : (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((op2 (e21) (e20)) = (e22)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e21) = (e23))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H22b zenon_H164 zenon_H16e zenon_H36a zenon_H1fa zenon_H1ac zenon_H175 zenon_H36d zenon_H293 zenon_H195 zenon_H15e zenon_H18e zenon_H187 zenon_H1f3 zenon_H1cd zenon_H1cc zenon_H19b zenon_H1e6 zenon_H1bd zenon_H1ec zenon_H244 zenon_H245 zenon_H1f7 zenon_H205 zenon_H22f zenon_H214 zenon_H1fd zenon_H16f zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H165 | zenon_intro zenon_H22c ]. % 51.35/51.51 apply (zenon_L117_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H17c | zenon_intro zenon_H22d ]. % 51.35/51.51 apply (zenon_L514_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H226 | zenon_intro zenon_H229 ]. % 51.35/51.51 apply (zenon_L531_); trivial. % 51.35/51.51 apply (zenon_L163_); trivial. % 51.35/51.51 (* end of lemma zenon_L532_ *) % 51.35/51.51 assert (zenon_L533_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((op2 (e21) (e20)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e22)) = (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 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e20) (e23)) = (e22)) -> (~((e22) = (e23))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H258 zenon_H210 zenon_H14e zenon_H14 zenon_H209 zenon_H16f zenon_H1fd zenon_H214 zenon_H22f zenon_H205 zenon_H245 zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H19b zenon_H1cc zenon_H1f3 zenon_H187 zenon_H18e zenon_H15e zenon_H195 zenon_H36d zenon_H1fa zenon_H36a zenon_H16e zenon_H164 zenon_H22b zenon_H24e zenon_H1d7 zenon_H1b1 zenon_H254 zenon_H23c zenon_H24b zenon_H21b zenon_H217 zenon_H21f zenon_H222 zenon_H1a7 zenon_H240 zenon_H13c zenon_H259 zenon_H1f7 zenon_H293 zenon_H175 zenon_H1ac. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.35/51.51 apply (zenon_L260_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.35/51.51 apply (zenon_L260_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.35/51.51 apply (zenon_L182_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.35/51.51 apply (zenon_L530_); trivial. % 51.35/51.51 apply (zenon_L532_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.35/51.51 apply (zenon_L429_); trivial. % 51.35/51.51 apply (zenon_L132_); trivial. % 51.35/51.51 (* end of lemma zenon_L533_ *) % 51.35/51.51 assert (zenon_L534_ : (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e20) = (e21))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e20)) = (e20)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e22) = (e23))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H258 zenon_H1f7 zenon_H254 zenon_H22f zenon_H16f zenon_H19b zenon_H205 zenon_H245 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H210 zenon_H1fa zenon_H187 zenon_H18e zenon_H15e zenon_H195 zenon_H1a7 zenon_H21f zenon_H1fd zenon_H217 zenon_H1f3 zenon_H1cc zenon_H1e6 zenon_H1ec zenon_H214 zenon_H240 zenon_H24e zenon_H13c zenon_H259 zenon_H2b6 zenon_H21b zenon_H21c zenon_H23c zenon_H14e zenon_H14 zenon_H209 zenon_H24b zenon_H175 zenon_H1ac. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.35/51.51 apply (zenon_L260_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.35/51.51 apply (zenon_L260_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.35/51.51 apply (zenon_L182_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.35/51.51 apply (zenon_L191_); trivial. % 51.35/51.51 apply (zenon_L192_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.35/51.51 apply (zenon_L263_); trivial. % 51.35/51.51 apply (zenon_L132_); trivial. % 51.35/51.51 (* end of lemma zenon_L534_ *) % 51.35/51.51 assert (zenon_L535_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e22)) = (e21)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((e21) = (e22))) -> ((op2 (e22) (e20)) = (e21)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e20) = (e21))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e20)) = (e20)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e22) = (e23))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H28d zenon_H168 zenon_H28e zenon_H15d zenon_H293 zenon_H222 zenon_H22b zenon_H164 zenon_H36a zenon_H36d zenon_H288 zenon_H26e zenon_H258 zenon_H1f7 zenon_H254 zenon_H22f zenon_H16f zenon_H19b zenon_H205 zenon_H245 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H210 zenon_H1fa zenon_H187 zenon_H18e zenon_H15e zenon_H195 zenon_H1a7 zenon_H21f zenon_H1fd zenon_H217 zenon_H1f3 zenon_H1cc zenon_H1e6 zenon_H1ec zenon_H214 zenon_H240 zenon_H24e zenon_H13c zenon_H259 zenon_H2b6 zenon_H21b zenon_H23c zenon_H14e zenon_H14 zenon_H209 zenon_H24b zenon_H1ac. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.35/51.51 apply (zenon_L116_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.35/51.51 apply (zenon_L117_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.35/51.51 apply (zenon_L118_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.35/51.51 apply (zenon_L116_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.35/51.51 apply (zenon_L533_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.35/51.51 apply (zenon_L223_); trivial. % 51.35/51.51 apply (zenon_L534_); trivial. % 51.35/51.51 (* end of lemma zenon_L535_ *) % 51.35/51.51 assert (zenon_L536_ : ((op2 (e22) (e20)) = (e22)) -> ((op2 (e22) (e20)) = (e23)) -> (~((e22) = (e23))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H176 zenon_H252 zenon_H1ac. % 51.35/51.51 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.35/51.51 cut (((e23) = (e23)) = ((e22) = (e23))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H1ac. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H1ad. % 51.35/51.51 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.35/51.51 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 51.35/51.51 congruence. % 51.35/51.51 cut (((op2 (e22) (e20)) = (e22)) = ((e23) = (e22))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H1ae. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H176. % 51.35/51.51 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.35/51.51 cut (((op2 (e22) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 51.35/51.51 congruence. % 51.35/51.51 exact (zenon_H2a0 zenon_H252). % 51.35/51.51 apply zenon_H171. apply refl_equal. % 51.35/51.51 apply zenon_H14c. apply refl_equal. % 51.35/51.51 apply zenon_H14c. apply refl_equal. % 51.35/51.51 (* end of lemma zenon_L536_ *) % 51.35/51.51 assert (zenon_L537_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e20) (e20)))) -> ((op2 (e23) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e20)) = (e20)) -> False). % 51.35/51.51 do 0 intro. intros zenon_H370 zenon_H203 zenon_H14e zenon_H13c. % 51.35/51.51 cut (((op2 (e23) (e21)) = (e20)) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (e20) (e20)))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H370. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H203. % 51.35/51.51 cut (((e20) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 51.35/51.51 cut (((op2 (e23) (e21)) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 51.35/51.51 congruence. % 51.35/51.51 elim (classic ((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [ zenon_intro zenon_H27a | zenon_intro zenon_H27b ]. % 51.35/51.51 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e23) (e21)) = (op2 (e23) (op2 (e23) (e23))))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H279. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H27a. % 51.35/51.51 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 51.35/51.51 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H14d]. % 51.35/51.51 congruence. % 51.35/51.51 apply (zenon_L112_); trivial. % 51.35/51.51 apply zenon_H27b. apply refl_equal. % 51.35/51.51 apply zenon_H27b. apply refl_equal. % 51.35/51.51 apply zenon_H15b. apply sym_equal. exact zenon_H13c. % 51.35/51.51 (* end of lemma zenon_L537_ *) % 51.35/51.51 assert (zenon_L538_ : ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e20) (e20)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H14 zenon_H16d zenon_H203 zenon_H13c zenon_H14e zenon_H240. % 51.35/51.51 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H371 | zenon_intro zenon_H1aa ]. % 51.35/51.51 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H240. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H371. % 51.35/51.51 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 51.35/51.51 cut (((op2 (e21) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H372]. % 51.35/51.51 congruence. % 51.35/51.51 cut (((e20) = (op2 (e23) (op2 (e23) (e23)))) = ((op2 (e21) (e20)) = (op2 (e20) (e20)))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H372. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H14. % 51.35/51.51 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H370]. % 51.35/51.51 cut (((e20) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H373]. % 51.35/51.51 congruence. % 51.35/51.51 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H371 | zenon_intro zenon_H1aa ]. % 51.35/51.51 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e20) = (op2 (e21) (e20)))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H373. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H371. % 51.35/51.51 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 51.35/51.51 cut (((op2 (e21) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H374]. % 51.35/51.51 congruence. % 51.35/51.51 exact (zenon_H374 zenon_H16d). % 51.35/51.51 apply zenon_H1aa. apply refl_equal. % 51.35/51.51 apply zenon_H1aa. apply refl_equal. % 51.35/51.51 apply (zenon_L537_); trivial. % 51.35/51.51 apply zenon_H1aa. apply refl_equal. % 51.35/51.51 apply zenon_H1aa. apply refl_equal. % 51.35/51.51 (* end of lemma zenon_L538_ *) % 51.35/51.51 assert (zenon_L539_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H240 zenon_H13c zenon_H16d zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.35/51.51 apply (zenon_L151_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.35/51.51 apply (zenon_L538_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.35/51.51 apply (zenon_L153_); trivial. % 51.35/51.51 apply (zenon_L154_); trivial. % 51.35/51.51 (* end of lemma zenon_L539_ *) % 51.35/51.51 assert (zenon_L540_ : (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e11) (e11)) = (e12)) -> ((op2 (e21) (e21)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H375 zenon_H349 zenon_H2c6 zenon_H17c zenon_H15e zenon_H2e7 zenon_H14e. % 51.35/51.51 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H375. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H349. % 51.35/51.51 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H376]. % 51.35/51.51 cut (((h4 (e12)) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H377]. % 51.35/51.51 congruence. % 51.35/51.51 elim (classic ((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [ zenon_intro zenon_H378 | zenon_intro zenon_H379 ]. % 51.35/51.51 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11)))) = ((h4 (e12)) = (h4 (op1 (e11) (e11))))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H377. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H378. % 51.35/51.51 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H379]. % 51.35/51.51 cut (((h4 (op1 (e11) (e11))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H37a]. % 51.35/51.51 congruence. % 51.35/51.51 cut (((op1 (e11) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H37b]. % 51.35/51.51 congruence. % 51.35/51.51 exact (zenon_H37b zenon_H2c6). % 51.35/51.51 apply zenon_H379. apply refl_equal. % 51.35/51.51 apply zenon_H379. apply refl_equal. % 51.35/51.51 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H37c | zenon_intro zenon_H37d ]. % 51.35/51.51 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e11)) (h4 (e11))))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H376. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H37c. % 51.35/51.51 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H37d]. % 51.35/51.51 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H37e]. % 51.35/51.51 congruence. % 51.35/51.51 cut (((op2 (e21) (e21)) = (e22)) = ((op2 (h4 (e11)) (h4 (e11))) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H37e. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H17c. % 51.35/51.51 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H37f]. % 51.35/51.51 cut (((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H380]. % 51.35/51.51 congruence. % 51.35/51.51 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H37c | zenon_intro zenon_H37d ]. % 51.35/51.51 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H380. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H37c. % 51.35/51.51 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H37d]. % 51.35/51.51 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H381]. % 51.35/51.51 congruence. % 51.35/51.51 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 51.35/51.51 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 51.35/51.51 congruence. % 51.35/51.51 apply (zenon_L326_); trivial. % 51.35/51.51 apply (zenon_L326_); trivial. % 51.35/51.51 apply zenon_H37d. apply refl_equal. % 51.35/51.51 apply zenon_H37d. apply refl_equal. % 51.35/51.51 exact (zenon_H37f zenon_H15e). % 51.35/51.51 apply zenon_H37d. apply refl_equal. % 51.35/51.51 apply zenon_H37d. apply refl_equal. % 51.35/51.51 (* end of lemma zenon_L540_ *) % 51.35/51.51 assert (zenon_L541_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e11) (e10)) = (e11)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e21) (e21)) = (e22)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H341 zenon_H10b zenon_H108 zenon_H14e zenon_H2e7 zenon_H15e zenon_H17c zenon_H349 zenon_H375 zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H49 zenon_H7c zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H2c zenon_H1c zenon_Hab. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.51 apply (zenon_L99_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.51 apply (zenon_L540_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.51 apply (zenon_L333_); trivial. % 51.35/51.51 apply (zenon_L34_); trivial. % 51.35/51.51 (* end of lemma zenon_L541_ *) % 51.35/51.51 assert (zenon_L542_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (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) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e21) (e21)) = (e22)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> (~((e10) = (e12))) -> ((op1 (e11) (e12)) = (e10)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H341 zenon_H8c zenon_H19 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hf8 zenon_H46 zenon_H45 zenon_H125 zenon_Hcf zenon_Ha2 zenon_H9e zenon_H95 zenon_Haf zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_Hde zenon_Hd3 zenon_Hda zenon_H2d1 zenon_H24 zenon_H23 zenon_H2c9 zenon_H42 zenon_H90 zenon_H2be zenon_Hb0 zenon_H2db zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H14e zenon_H2e7 zenon_H15e zenon_H17c zenon_H349 zenon_H375 zenon_H35 zenon_H126 zenon_H2c zenon_H1c zenon_Hab. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.51 apply (zenon_L313_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.51 apply (zenon_L540_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.51 apply (zenon_L454_); trivial. % 51.35/51.51 apply (zenon_L34_); trivial. % 51.35/51.51 (* end of lemma zenon_L542_ *) % 51.35/51.51 assert (zenon_L543_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.35/51.51 do 0 intro. intros zenon_Hff zenon_He8 zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hde zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c zenon_H108 zenon_H23 zenon_Hfb zenon_H3d zenon_H11a zenon_H49 zenon_H4b. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.51 apply (zenon_L317_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.51 apply (zenon_L407_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.51 apply (zenon_L427_); trivial. % 51.35/51.51 apply (zenon_L15_); trivial. % 51.35/51.51 (* end of lemma zenon_L543_ *) % 51.35/51.51 assert (zenon_L544_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e21) (e21)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((e11) = (e12))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e12) = (e13))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H32a zenon_H2be zenon_Hfe zenon_H2b zenon_H2e1 zenon_H2ba zenon_Ha2 zenon_H2ff zenon_H375 zenon_H349 zenon_H17c zenon_H15e zenon_H2e7 zenon_H14e zenon_H10b zenon_H341 zenon_Hff zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hde zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c zenon_H108 zenon_H23 zenon_Hfb zenon_H3d zenon_H11a zenon_H4b. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.51 apply (zenon_L7_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.51 apply (zenon_L281_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.51 apply (zenon_L282_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.51 apply (zenon_L7_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.51 apply (zenon_L99_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.51 apply (zenon_L541_); trivial. % 51.35/51.51 apply (zenon_L543_); trivial. % 51.35/51.51 (* end of lemma zenon_L544_ *) % 51.35/51.51 assert (zenon_L545_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e21) (e21)) = (e22)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H13b zenon_H318 zenon_H2db zenon_H305 zenon_H311 zenon_H30d zenon_H314 zenon_H2e0 zenon_H2ce zenon_H2d4 zenon_H2d1 zenon_H327 zenon_H345 zenon_H33e zenon_H33a zenon_H31e zenon_H31b zenon_H341 zenon_H14e zenon_H2e7 zenon_H15e zenon_H17c zenon_H349 zenon_H375 zenon_H2ff zenon_H2be zenon_H32a zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.51 apply (zenon_L7_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.51 apply (zenon_L281_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.51 apply (zenon_L282_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.51 apply (zenon_L7_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.51 apply (zenon_L325_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.51 apply (zenon_L317_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.51 apply (zenon_L317_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.51 apply (zenon_L12_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.51 apply (zenon_L283_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.51 apply (zenon_L541_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.51 apply (zenon_L455_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.51 apply (zenon_L359_); trivial. % 51.35/51.51 apply (zenon_L33_); trivial. % 51.35/51.51 apply (zenon_L369_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.51 apply (zenon_L541_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.51 apply (zenon_L479_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.51 apply (zenon_L485_); trivial. % 51.35/51.51 apply (zenon_L33_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.51 apply (zenon_L283_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.51 apply (zenon_L541_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.51 apply (zenon_L479_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.51 apply (zenon_L359_); trivial. % 51.35/51.51 apply (zenon_L33_); trivial. % 51.35/51.51 apply (zenon_L377_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.51 apply (zenon_L494_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.51 apply (zenon_L283_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.51 apply (zenon_L542_); trivial. % 51.35/51.51 apply (zenon_L377_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.51 apply (zenon_L378_); trivial. % 51.35/51.51 apply (zenon_L335_); trivial. % 51.35/51.51 apply (zenon_L384_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.35/51.51 apply (zenon_L426_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.51 apply (zenon_L7_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.51 apply (zenon_L281_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.51 apply (zenon_L282_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.51 apply (zenon_L7_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.51 apply (zenon_L325_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.51 apply (zenon_L11_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.51 apply (zenon_L11_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.51 apply (zenon_L502_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.51 apply (zenon_L544_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.51 apply (zenon_L479_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.51 apply (zenon_L482_); trivial. % 51.35/51.51 apply (zenon_L33_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.51 apply (zenon_L544_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.51 apply (zenon_L492_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.51 apply (zenon_L482_); trivial. % 51.35/51.51 apply (zenon_L33_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.51 apply (zenon_L283_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.51 apply (zenon_L542_); trivial. % 51.35/51.51 apply (zenon_L377_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.51 apply (zenon_L378_); trivial. % 51.35/51.51 apply (zenon_L15_); trivial. % 51.35/51.51 apply (zenon_L384_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.35/51.51 apply (zenon_L544_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.35/51.51 apply (zenon_L512_); trivial. % 51.35/51.51 apply (zenon_L82_); trivial. % 51.35/51.51 apply (zenon_L85_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.35/51.51 apply (zenon_L4_); trivial. % 51.35/51.51 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.35/51.51 apply (zenon_L109_); trivial. % 51.35/51.51 apply (zenon_L47_); trivial. % 51.35/51.51 (* end of lemma zenon_L545_ *) % 51.35/51.51 assert (zenon_L546_ : ((op2 (e21) (e22)) = (e20)) -> ((op2 (e21) (e22)) = (e22)) -> (~((e20) = (e22))) -> False). % 51.35/51.51 do 0 intro. intros zenon_H277 zenon_H17f zenon_H16f. % 51.35/51.51 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H170 | zenon_intro zenon_H171 ]. % 51.35/51.51 cut (((e22) = (e22)) = ((e20) = (e22))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H16f. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H170. % 51.35/51.51 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.35/51.51 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 51.35/51.51 congruence. % 51.35/51.51 cut (((op2 (e21) (e22)) = (e20)) = ((e22) = (e20))). % 51.35/51.51 intro zenon_D_pnotp. % 51.35/51.51 apply zenon_H172. % 51.35/51.51 rewrite <- zenon_D_pnotp. % 51.35/51.51 exact zenon_H277. % 51.35/51.51 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 51.35/51.52 cut (((op2 (e21) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 51.35/51.52 congruence. % 51.35/51.52 exact (zenon_H185 zenon_H17f). % 51.35/51.52 apply zenon_H16c. apply refl_equal. % 51.35/51.52 apply zenon_H171. apply refl_equal. % 51.35/51.52 apply zenon_H171. apply refl_equal. % 51.35/51.52 (* end of lemma zenon_L546_ *) % 51.35/51.52 assert (zenon_L547_ : (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((e20) = (e22))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e21))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H2a6 zenon_H13c zenon_H240 zenon_H26d zenon_H187 zenon_H14 zenon_H15e zenon_H16f zenon_H13b zenon_H318 zenon_H2db zenon_H305 zenon_H311 zenon_H30d zenon_H314 zenon_H2e0 zenon_H2ce zenon_H2d4 zenon_H2d1 zenon_H327 zenon_H345 zenon_H33e zenon_H33a zenon_H31e zenon_H31b zenon_H341 zenon_H2e7 zenon_H349 zenon_H375 zenon_H2ff zenon_H2be zenon_H32a zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H22b zenon_H164 zenon_H36a zenon_H36d zenon_H293 zenon_H195 zenon_H18e zenon_H1f3 zenon_H19b zenon_H1bd zenon_H22f zenon_H214 zenon_H1fd zenon_H209 zenon_H210 zenon_H22e zenon_H1fa zenon_H1ac zenon_H205 zenon_H245 zenon_H244 zenon_H1ec zenon_H1cc zenon_H1cd zenon_H1e6 zenon_H175 zenon_H1f7 zenon_H14e. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H16d | zenon_intro zenon_H2ac ]. % 51.35/51.52 apply (zenon_L539_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H2a1 | zenon_intro zenon_H2ad ]. % 51.35/51.52 apply (zenon_L246_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H277 | zenon_intro zenon_H1a8 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H16e | zenon_intro zenon_H231 ]. % 51.35/51.52 apply (zenon_L532_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17c | zenon_intro zenon_H232 ]. % 51.35/51.52 apply (zenon_L545_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17f | zenon_intro zenon_H186 ]. % 51.35/51.52 apply (zenon_L546_); trivial. % 51.35/51.52 apply (zenon_L124_); trivial. % 51.35/51.52 apply (zenon_L243_); trivial. % 51.35/51.52 (* end of lemma zenon_L547_ *) % 51.35/51.52 assert (zenon_L548_ : (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op2 (e21) (e22)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H382 zenon_H13 zenon_H126 zenon_H277 zenon_H14 zenon_H2e7 zenon_H14e zenon_H349 zenon_H15e. % 51.35/51.52 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H382. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H13. % 51.35/51.52 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H383]. % 51.35/51.52 cut (((h4 (e10)) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H384]. % 51.35/51.52 congruence. % 51.35/51.52 elim (classic ((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [ zenon_intro zenon_H385 | zenon_intro zenon_H386 ]. % 51.35/51.52 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12)))) = ((h4 (e10)) = (h4 (op1 (e11) (e12))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H384. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H385. % 51.35/51.52 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H386]. % 51.35/51.52 cut (((h4 (op1 (e11) (e12))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H387]. % 51.35/51.52 congruence. % 51.35/51.52 cut (((op1 (e11) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H388]. % 51.35/51.52 congruence. % 51.35/51.52 exact (zenon_H388 zenon_H126). % 51.35/51.52 apply zenon_H386. apply refl_equal. % 51.35/51.52 apply zenon_H386. apply refl_equal. % 51.35/51.52 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H389 | zenon_intro zenon_H38a ]. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e12))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H383. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H389. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H38a]. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H38b]. % 51.35/51.52 congruence. % 51.35/51.52 cut (((op2 (e21) (e22)) = (e20)) = ((op2 (h4 (e11)) (h4 (e12))) = (op2 (e23) (op2 (e23) (e23))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H38b. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H277. % 51.35/51.52 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 51.35/51.52 cut (((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H38c]. % 51.35/51.52 congruence. % 51.35/51.52 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H389 | zenon_intro zenon_H38a ]. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H38c. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H389. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H38a]. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H38d]. % 51.35/51.52 congruence. % 51.35/51.52 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.35/51.52 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 51.35/51.52 congruence. % 51.35/51.52 apply (zenon_L326_); trivial. % 51.35/51.52 apply (zenon_L487_); trivial. % 51.35/51.52 apply zenon_H38a. apply refl_equal. % 51.35/51.52 apply zenon_H38a. apply refl_equal. % 51.35/51.52 exact (zenon_H148 zenon_H14). % 51.35/51.52 apply zenon_H38a. apply refl_equal. % 51.35/51.52 apply zenon_H38a. apply refl_equal. % 51.35/51.52 (* end of lemma zenon_L548_ *) % 51.35/51.52 assert (zenon_L549_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.52 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3d zenon_Hcb zenon_Ha3 zenon_H42 zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H50 zenon_H95 zenon_H49 zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.35/51.52 apply (zenon_L39_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.35/51.52 apply (zenon_L286_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.35/51.52 apply (zenon_L41_); trivial. % 51.35/51.52 apply (zenon_L24_); trivial. % 51.35/51.52 (* end of lemma zenon_L549_ *) % 51.35/51.52 assert (zenon_L550_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.35/51.52 do 0 intro. intros zenon_Hf8 zenon_H108 zenon_H46 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hcf zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_Hb8 zenon_Hc8 zenon_H50 zenon_H42. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.52 apply (zenon_L328_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.52 apply (zenon_L13_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.52 apply (zenon_L549_); trivial. % 51.35/51.52 apply (zenon_L17_); trivial. % 51.35/51.52 (* end of lemma zenon_L550_ *) % 51.35/51.52 assert (zenon_L551_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H2e0 zenon_H10e zenon_H15e zenon_H349 zenon_H14e zenon_H2e7 zenon_H14 zenon_H277 zenon_H13 zenon_H382 zenon_Hf8 zenon_H108 zenon_H46 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hcf zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_Hb8 zenon_Hc8 zenon_H42. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.52 apply (zenon_L74_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.52 apply (zenon_L283_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.52 apply (zenon_L548_); trivial. % 51.35/51.52 apply (zenon_L550_); trivial. % 51.35/51.52 (* end of lemma zenon_L551_ *) % 51.35/51.52 assert (zenon_L552_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H2e0 zenon_H10e zenon_H15e zenon_H349 zenon_H14e zenon_H2e7 zenon_H14 zenon_H277 zenon_H13 zenon_H382 zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H3d zenon_H131 zenon_H12c zenon_H108 zenon_H128 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H54 zenon_Haf zenon_H42 zenon_H4b zenon_Hb5 zenon_H8c zenon_Hde zenon_H1c zenon_H19 zenon_Hc2. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.52 apply (zenon_L74_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.52 apply (zenon_L283_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.52 apply (zenon_L548_); trivial. % 51.35/51.52 apply (zenon_L405_); trivial. % 51.35/51.52 (* end of lemma zenon_L552_ *) % 51.35/51.52 assert (zenon_L553_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e12) = (e13))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H32a zenon_H2b zenon_H2ba zenon_H2c zenon_H2be zenon_Hff zenon_H23 zenon_H42 zenon_Hc8 zenon_Hb8 zenon_Hcb zenon_Hb5 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c zenon_H45 zenon_H108 zenon_Hf8 zenon_H382 zenon_H13 zenon_H277 zenon_H14 zenon_H2e7 zenon_H14e zenon_H349 zenon_H15e zenon_H10e zenon_H2e0 zenon_H3d zenon_H11a zenon_H4b. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.52 apply (zenon_L7_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.52 apply (zenon_L281_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.52 apply (zenon_L282_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.52 apply (zenon_L317_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.52 apply (zenon_L551_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.52 apply (zenon_L427_); trivial. % 51.35/51.52 apply (zenon_L15_); trivial. % 51.35/51.52 (* end of lemma zenon_L553_ *) % 51.35/51.52 assert (zenon_L554_ : ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.52 do 0 intro. intros zenon_Hf1 zenon_H65 zenon_H2c9 zenon_H30b zenon_H330 zenon_H46 zenon_H327 zenon_Hcf zenon_Hbe zenon_H95 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_Hde zenon_H8c zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.35/51.52 apply (zenon_L439_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.35/51.52 apply (zenon_L42_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.35/51.52 apply (zenon_L373_); trivial. % 51.35/51.52 apply (zenon_L37_); trivial. % 51.35/51.52 (* end of lemma zenon_L554_ *) % 51.35/51.52 assert (zenon_L555_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H33e zenon_H10b zenon_H2c9 zenon_He2 zenon_H2e1 zenon_H8c zenon_H1c zenon_Hc2 zenon_H327 zenon_H2d1 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hb0 zenon_Hda zenon_H49 zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H35 zenon_H42 zenon_Hd3 zenon_H65 zenon_Hde zenon_H3d zenon_H9e zenon_H19. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.52 apply (zenon_L75_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.35/51.52 apply (zenon_L282_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.35/51.52 apply (zenon_L333_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.35/51.52 apply (zenon_L334_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.35/51.52 apply (zenon_L39_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.35/51.52 apply (zenon_L554_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.35/51.52 apply (zenon_L41_); trivial. % 51.35/51.52 apply (zenon_L24_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.52 apply (zenon_L451_); trivial. % 51.35/51.52 apply (zenon_L452_); trivial. % 51.35/51.52 (* end of lemma zenon_L555_ *) % 51.35/51.52 assert (zenon_L556_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H90 zenon_H35 zenon_H49 zenon_H42 zenon_H51 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H335 zenon_H11a zenon_H46 zenon_H2ce zenon_H19 zenon_H8c. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.35/51.52 apply (zenon_L16_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.35/51.52 apply (zenon_L17_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.35/51.52 apply (zenon_L443_); trivial. % 51.35/51.52 apply (zenon_L24_); trivial. % 51.35/51.52 (* end of lemma zenon_L556_ *) % 51.35/51.52 assert (zenon_L557_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e12)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.52 do 0 intro. intros zenon_Hcf zenon_H2ce zenon_H46 zenon_H11a zenon_H335 zenon_H65 zenon_H72 zenon_Hbe zenon_H8c zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H19. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.35/51.52 apply (zenon_L556_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.35/51.52 apply (zenon_L40_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.35/51.52 apply (zenon_L52_); trivial. % 51.35/51.52 apply (zenon_L37_); trivial. % 51.35/51.52 (* end of lemma zenon_L557_ *) % 51.35/51.52 assert (zenon_L558_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.52 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3d zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H72 zenon_H65 zenon_H335 zenon_H11a zenon_H46 zenon_H2ce zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.35/51.52 apply (zenon_L39_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.35/51.52 apply (zenon_L557_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.35/51.52 apply (zenon_L41_); trivial. % 51.35/51.52 apply (zenon_L24_); trivial. % 51.35/51.52 (* end of lemma zenon_L558_ *) % 51.35/51.52 assert (zenon_L559_ : (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((e20) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.35/51.52 do 0 intro. intros zenon_H2a6 zenon_H210 zenon_H209 zenon_H13c zenon_H240 zenon_H1fd zenon_H214 zenon_H26d zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H32a zenon_H2be zenon_H382 zenon_H13 zenon_H14 zenon_H2e7 zenon_H349 zenon_H15e zenon_H2e0 zenon_H31b zenon_H31e zenon_H341 zenon_H33e zenon_H345 zenon_H327 zenon_H2d1 zenon_H33a zenon_H2d4 zenon_H2ce zenon_H314 zenon_H30d zenon_H2ff zenon_H311 zenon_H305 zenon_H2db zenon_H318 zenon_H13b zenon_H1fa zenon_H1ac zenon_H205 zenon_H245 zenon_H244 zenon_H1ec zenon_H1cc zenon_H1cd zenon_H1e6 zenon_H175 zenon_H1f7 zenon_H14e. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H16d | zenon_intro zenon_H2ac ]. % 51.35/51.52 apply (zenon_L539_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2ac); [ zenon_intro zenon_H2a1 | zenon_intro zenon_H2ad ]. % 51.35/51.52 apply (zenon_L246_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2ad); [ zenon_intro zenon_H277 | zenon_intro zenon_H1a8 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.52 apply (zenon_L7_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.52 apply (zenon_L281_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.52 apply (zenon_L282_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.52 apply (zenon_L7_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.52 apply (zenon_L325_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.52 apply (zenon_L11_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.52 apply (zenon_L11_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.52 apply (zenon_L12_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.52 apply (zenon_L283_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.52 apply (zenon_L548_); trivial. % 51.35/51.52 apply (zenon_L377_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.52 apply (zenon_L551_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.52 apply (zenon_L9_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.52 apply (zenon_L478_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.52 apply (zenon_L333_); trivial. % 51.35/51.52 apply (zenon_L34_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.52 apply (zenon_L485_); trivial. % 51.35/51.52 apply (zenon_L33_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.52 apply (zenon_L283_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.52 apply (zenon_L548_); trivial. % 51.35/51.52 apply (zenon_L377_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.52 apply (zenon_L552_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.52 apply (zenon_L492_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.52 apply (zenon_L493_); trivial. % 51.35/51.52 apply (zenon_L33_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.52 apply (zenon_L283_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.52 apply (zenon_L548_); trivial. % 51.35/51.52 apply (zenon_L377_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.52 apply (zenon_L378_); trivial. % 51.35/51.52 apply (zenon_L15_); trivial. % 51.35/51.52 apply (zenon_L384_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.35/51.52 apply (zenon_L426_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.52 apply (zenon_L7_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.52 apply (zenon_L281_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.52 apply (zenon_L282_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.52 apply (zenon_L7_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.52 apply (zenon_L325_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.52 apply (zenon_L317_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.52 apply (zenon_L317_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.52 apply (zenon_L502_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.52 apply (zenon_L553_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.52 apply (zenon_L310_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.52 apply (zenon_L555_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.52 apply (zenon_L13_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.52 apply (zenon_L471_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.52 apply (zenon_L80_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.52 apply (zenon_L474_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.52 apply (zenon_L558_); trivial. % 51.35/51.52 apply (zenon_L452_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.52 apply (zenon_L333_); trivial. % 51.35/51.52 apply (zenon_L34_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.52 apply (zenon_L482_); trivial. % 51.35/51.52 apply (zenon_L33_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.52 apply (zenon_L283_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.52 apply (zenon_L548_); trivial. % 51.35/51.52 apply (zenon_L377_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.52 apply (zenon_L553_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.52 apply (zenon_L316_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.52 apply (zenon_L453_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.52 apply (zenon_L13_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.52 apply (zenon_L471_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.52 apply (zenon_L80_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.52 apply (zenon_L491_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.52 apply (zenon_L556_); trivial. % 51.35/51.52 apply (zenon_L452_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.52 apply (zenon_L333_); trivial. % 51.35/51.52 apply (zenon_L34_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.52 apply (zenon_L482_); trivial. % 51.35/51.52 apply (zenon_L33_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.52 apply (zenon_L283_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.52 apply (zenon_L548_); trivial. % 51.35/51.52 apply (zenon_L377_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.52 apply (zenon_L378_); trivial. % 51.35/51.52 apply (zenon_L335_); trivial. % 51.35/51.52 apply (zenon_L384_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.35/51.52 apply (zenon_L553_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.35/51.52 apply (zenon_L512_); trivial. % 51.35/51.52 apply (zenon_L82_); trivial. % 51.35/51.52 apply (zenon_L85_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.35/51.52 apply (zenon_L4_); trivial. % 51.35/51.52 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.35/51.52 apply (zenon_L109_); trivial. % 51.35/51.52 apply (zenon_L47_); trivial. % 51.35/51.52 apply (zenon_L243_); trivial. % 51.35/51.52 (* end of lemma zenon_L559_ *) % 51.35/51.52 assert (zenon_L560_ : (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op1 (e11) (e13)) = (e13)) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.35/51.52 do 0 intro. intros zenon_H38e zenon_H51 zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea. % 51.35/51.52 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H38e. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H2ea. % 51.35/51.52 cut (((e23) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H38f]. % 51.35/51.52 cut (((h4 (e13)) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H390]. % 51.35/51.52 congruence. % 51.35/51.52 elim (classic ((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [ zenon_intro zenon_H391 | zenon_intro zenon_H392 ]. % 51.35/51.52 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13)))) = ((h4 (e13)) = (h4 (op1 (e11) (e13))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H390. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H391. % 51.35/51.52 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H392]. % 51.35/51.52 cut (((h4 (op1 (e11) (e13))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H393]. % 51.35/51.52 congruence. % 51.35/51.52 cut (((op1 (e11) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 51.35/51.52 congruence. % 51.35/51.52 exact (zenon_H52 zenon_H51). % 51.35/51.52 apply zenon_H392. apply refl_equal. % 51.35/51.52 apply zenon_H392. apply refl_equal. % 51.35/51.52 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H394 | zenon_intro zenon_H395 ]. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((e23) = (op2 (h4 (e11)) (h4 (e13))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H38f. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H394. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H395]. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e13))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H396]. % 51.35/51.52 congruence. % 51.35/51.52 cut (((op2 (e21) (e23)) = (e23)) = ((op2 (h4 (e11)) (h4 (e13))) = (e23))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H396. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H1bc. % 51.35/51.52 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.35/51.52 cut (((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H397]. % 51.35/51.52 congruence. % 51.35/51.52 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H394 | zenon_intro zenon_H395 ]. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))). % 51.35/51.52 intro zenon_D_pnotp. % 51.35/51.52 apply zenon_H397. % 51.35/51.52 rewrite <- zenon_D_pnotp. % 51.35/51.52 exact zenon_H394. % 51.35/51.52 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H395]. % 51.35/51.53 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H398]. % 51.35/51.53 congruence. % 51.35/51.53 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H399]. % 51.35/51.53 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 51.35/51.53 congruence. % 51.35/51.53 apply (zenon_L326_); trivial. % 51.35/51.53 exact (zenon_H399 zenon_H2ea). % 51.35/51.53 apply zenon_H395. apply refl_equal. % 51.35/51.53 apply zenon_H395. apply refl_equal. % 51.35/51.53 apply zenon_H14c. apply refl_equal. % 51.35/51.53 apply zenon_H395. apply refl_equal. % 51.35/51.53 apply zenon_H395. apply refl_equal. % 51.35/51.53 (* end of lemma zenon_L560_ *) % 51.35/51.53 assert (zenon_L561_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.53 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H2ea zenon_H14e zenon_H2e7 zenon_H1bc zenon_H38e zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.35/51.53 apply (zenon_L15_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.35/51.53 apply (zenon_L36_); trivial. % 51.35/51.53 apply (zenon_L37_); trivial. % 51.35/51.53 (* end of lemma zenon_L561_ *) % 51.35/51.53 assert (zenon_L562_ : ((op1 (e11) (e12)) = (e13)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.53 do 0 intro. intros zenon_Ha3 zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea zenon_Hc2 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H131 zenon_Hbe zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_H8c zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H2db zenon_H23 zenon_H24 zenon_H324 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H62 zenon_H3d zenon_H19. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.35/51.53 apply (zenon_L561_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.35/51.53 apply (zenon_L40_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.35/51.53 apply (zenon_L394_); trivial. % 51.35/51.53 apply (zenon_L37_); trivial. % 51.35/51.53 (* end of lemma zenon_L562_ *) % 51.35/51.53 assert (zenon_L563_ : (~((e11) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H3d zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_Hde zenon_Hcb zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hc2 zenon_H2ea zenon_H14e zenon_H2e7 zenon_H1bc zenon_H38e zenon_Ha3 zenon_H19 zenon_H8c. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.35/51.53 apply (zenon_L16_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.35/51.53 apply (zenon_L549_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.35/51.53 apply (zenon_L562_); trivial. % 51.35/51.53 apply (zenon_L24_); trivial. % 51.35/51.53 (* end of lemma zenon_L563_ *) % 51.35/51.53 assert (zenon_L564_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.35/51.53 do 0 intro. intros zenon_Hf8 zenon_H46 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H3d zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_Hde zenon_Hcb zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_H131 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H7c zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L328_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L13_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.35/51.53 apply (zenon_L39_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.35/51.53 apply (zenon_L563_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.35/51.53 apply (zenon_L41_); trivial. % 51.35/51.53 apply (zenon_L24_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 (* end of lemma zenon_L564_ *) % 51.35/51.53 assert (zenon_L565_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.35/51.53 do 0 intro. intros zenon_Hf8 zenon_H108 zenon_H46 zenon_H45 zenon_H19 zenon_H3d zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H4b zenon_Hb5 zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L328_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L13_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_L561_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 (* end of lemma zenon_L565_ *) % 51.35/51.53 assert (zenon_L566_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.35/51.53 do 0 intro. intros zenon_Hfb zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_H131 zenon_H128 zenon_Hda zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H2db zenon_H23 zenon_H24 zenon_H324 zenon_Hc2 zenon_H8c zenon_Hf8 zenon_H108 zenon_H46 zenon_H45 zenon_H19 zenon_H3d zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H4b zenon_Hb5 zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.53 apply (zenon_L317_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.53 apply (zenon_L328_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.53 apply (zenon_L564_); trivial. % 51.35/51.53 apply (zenon_L565_); trivial. % 51.35/51.53 (* end of lemma zenon_L566_ *) % 51.35/51.53 assert (zenon_L567_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (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 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H341 zenon_H23 zenon_H2db zenon_H125 zenon_H24 zenon_H2c5 zenon_Hff zenon_H2ea zenon_H14e zenon_H2e7 zenon_H1bc zenon_H38e zenon_H345 zenon_H33e zenon_H10b zenon_He1 zenon_H2c9 zenon_H30b zenon_Hf3 zenon_Hf0 zenon_H327 zenon_Hde zenon_Hd3 zenon_Hda zenon_H3d zenon_Hcb zenon_H42 zenon_Hb5 zenon_H4b zenon_H2d1 zenon_H7d zenon_H90 zenon_H46 zenon_H33a zenon_H2ce zenon_H72 zenon_Haf zenon_H54 zenon_H95 zenon_H65 zenon_H9e zenon_Hb0 zenon_Hcf zenon_H305 zenon_H2be zenon_H31e zenon_Hec zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H45 zenon_He2 zenon_Hea zenon_H31b zenon_H113 zenon_Hf8 zenon_H2e0 zenon_Hf6 zenon_Hfb zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H318 zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H49 zenon_H7c zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H2c zenon_H1c zenon_Hab. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.53 apply (zenon_L325_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L555_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L299_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_L471_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.53 apply (zenon_L333_); trivial. % 51.35/51.53 apply (zenon_L34_); trivial. % 51.35/51.53 (* end of lemma zenon_L567_ *) % 51.35/51.53 assert (zenon_L568_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e10)) = (e10)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e11) = (e13))) -> ((op1 (e11) (e12)) = (e11)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.35/51.53 do 0 intro. intros zenon_Hf8 zenon_H42 zenon_H33 zenon_H46 zenon_H45 zenon_H3d zenon_H129 zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L12_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L13_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_L465_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 (* end of lemma zenon_L568_ *) % 51.35/51.53 assert (zenon_L569_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H341 zenon_H23 zenon_H2db zenon_H125 zenon_H24 zenon_H2c5 zenon_Hff zenon_H2ea zenon_H14e zenon_H2e7 zenon_H1bc zenon_H38e zenon_Hb5 zenon_H4b zenon_Haf zenon_H54 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Hb0 zenon_H3d zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H45 zenon_H33e zenon_H10b zenon_H2c9 zenon_H126 zenon_H327 zenon_H2d1 zenon_H46 zenon_H33a zenon_H2ce zenon_H72 zenon_H2be zenon_H31e zenon_Hda zenon_Hea zenon_He1 zenon_H30b zenon_H31b zenon_H113 zenon_Hf8 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_Hfb zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H305 zenon_H318 zenon_H90 zenon_H42 zenon_Hd3 zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H49 zenon_H7c zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H2c zenon_H1c zenon_Hab. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.53 apply (zenon_L325_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L496_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L299_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_L561_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.53 apply (zenon_L333_); trivial. % 51.35/51.53 apply (zenon_L34_); trivial. % 51.35/51.53 (* end of lemma zenon_L569_ *) % 51.35/51.53 assert (zenon_L570_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.35/51.53 do 0 intro. intros zenon_Hf8 zenon_H33 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H3d zenon_Hcb zenon_H42 zenon_H33e zenon_H10b zenon_H7c zenon_He1 zenon_H2c9 zenon_H30b zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H90 zenon_H35 zenon_Hde zenon_Hb5 zenon_H4b zenon_Hcf zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H11a zenon_H46 zenon_H2ce zenon_H9e zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L12_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L13_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_L464_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 (* end of lemma zenon_L570_ *) % 51.35/51.53 assert (zenon_L571_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H318 zenon_H2ea zenon_H14e zenon_H2e7 zenon_H1bc zenon_H38e zenon_H9e zenon_H2ce zenon_H46 zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hcf zenon_H4b zenon_Hb5 zenon_Hde zenon_H35 zenon_H90 zenon_Haf zenon_H2c zenon_Hab zenon_H49 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H2c9 zenon_He1 zenon_H7c zenon_H10b zenon_H33e zenon_H42 zenon_Hcb zenon_H3d zenon_Hc2 zenon_H1c zenon_H8c zenon_H45 zenon_H33 zenon_Hf8 zenon_H11a zenon_H125 zenon_H54 zenon_H19. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L74_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_L570_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L482_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 (* end of lemma zenon_L571_ *) % 51.35/51.53 assert (zenon_L572_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e11)) = (e12)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.35/51.53 do 0 intro. intros zenon_H318 zenon_H305 zenon_H10e zenon_H123 zenon_H311 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_H7d zenon_Hf8 zenon_H113 zenon_H31b zenon_Hea zenon_H31e zenon_H2be zenon_H72 zenon_H33a zenon_H2c6 zenon_H2d1 zenon_H2e1 zenon_He2 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H3d zenon_Hcb zenon_H42 zenon_H33e zenon_H10b zenon_H7c zenon_He1 zenon_H2c9 zenon_H30b zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H90 zenon_H35 zenon_Hde zenon_Hb5 zenon_H4b zenon_Hcf zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H11a zenon_H46 zenon_H2ce zenon_H9e zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L555_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L13_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_L464_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 (* end of lemma zenon_L572_ *) % 51.35/51.53 assert (zenon_L573_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((op2 (e21) (e23)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e12) = (e13))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H32a zenon_H2be zenon_Hfe zenon_H2b zenon_H10b zenon_H2ff zenon_H2ba zenon_H2e1 zenon_H131 zenon_H128 zenon_H12c zenon_H2db zenon_H24 zenon_H324 zenon_Ha2 zenon_H65 zenon_H95 zenon_Haf zenon_H38e zenon_H1bc zenon_H2e7 zenon_H14e zenon_H2ea zenon_Hff zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hde zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c zenon_H108 zenon_H23 zenon_Hfb zenon_H3d zenon_H11a zenon_H4b. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.53 apply (zenon_L281_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.53 apply (zenon_L282_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.53 apply (zenon_L99_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.53 apply (zenon_L317_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.53 apply (zenon_L566_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.53 apply (zenon_L427_); trivial. % 51.35/51.53 apply (zenon_L335_); trivial. % 51.35/51.53 apply (zenon_L543_); trivial. % 51.35/51.53 (* end of lemma zenon_L573_ *) % 51.35/51.53 assert (zenon_L574_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H13b zenon_H318 zenon_H305 zenon_H311 zenon_H30d zenon_H314 zenon_H2e0 zenon_H2ce zenon_H2d4 zenon_H33a zenon_H2d1 zenon_H327 zenon_H33e zenon_H341 zenon_H31e zenon_H31b zenon_H2ea zenon_H14e zenon_H2e7 zenon_H1bc zenon_H38e zenon_H324 zenon_H2db zenon_H2ff zenon_H2be zenon_H32a zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H345 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.53 apply (zenon_L281_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.53 apply (zenon_L282_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.53 apply (zenon_L325_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.53 apply (zenon_L11_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.53 apply (zenon_L11_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.53 apply (zenon_L12_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.53 apply (zenon_L283_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L566_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_L455_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L359_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 apply (zenon_L369_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L74_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_L567_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L568_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.53 apply (zenon_L283_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L566_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_L567_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L359_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 apply (zenon_L377_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.53 apply (zenon_L12_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.53 apply (zenon_L299_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.53 apply (zenon_L561_); trivial. % 51.35/51.53 apply (zenon_L560_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.53 apply (zenon_L283_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L565_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_L569_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L359_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 apply (zenon_L377_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.53 apply (zenon_L378_); trivial. % 51.35/51.53 apply (zenon_L335_); trivial. % 51.35/51.53 apply (zenon_L384_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.35/51.53 apply (zenon_L426_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.53 apply (zenon_L281_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.53 apply (zenon_L282_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.53 apply (zenon_L325_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.53 apply (zenon_L317_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.53 apply (zenon_L317_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.53 apply (zenon_L571_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.53 apply (zenon_L283_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.53 apply (zenon_L501_); trivial. % 51.35/51.53 apply (zenon_L369_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.53 apply (zenon_L571_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.53 apply (zenon_L283_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L564_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.35/51.53 apply (zenon_L325_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.35/51.53 apply (zenon_L572_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.35/51.53 apply (zenon_L454_); trivial. % 51.35/51.53 apply (zenon_L34_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L482_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 apply (zenon_L377_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L565_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_L570_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L482_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.35/51.53 apply (zenon_L283_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.35/51.53 apply (zenon_L573_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.35/51.53 apply (zenon_L569_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.35/51.53 apply (zenon_L359_); trivial. % 51.35/51.53 apply (zenon_L33_); trivial. % 51.35/51.53 apply (zenon_L377_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.53 apply (zenon_L378_); trivial. % 51.35/51.53 apply (zenon_L335_); trivial. % 51.35/51.53 apply (zenon_L384_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.35/51.53 apply (zenon_L573_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.35/51.53 apply (zenon_L512_); trivial. % 51.35/51.53 apply (zenon_L82_); trivial. % 51.35/51.53 apply (zenon_L85_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.35/51.53 apply (zenon_L4_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.35/51.53 apply (zenon_L109_); trivial. % 51.35/51.53 apply (zenon_L47_); trivial. % 51.35/51.53 (* end of lemma zenon_L574_ *) % 51.35/51.53 assert (zenon_L575_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H175 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H345 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H32a zenon_H2be zenon_H2ff zenon_H2db zenon_H324 zenon_H38e zenon_H2e7 zenon_H2ea zenon_H31b zenon_H31e zenon_H341 zenon_H33e zenon_H327 zenon_H2d1 zenon_H33a zenon_H2d4 zenon_H2ce zenon_H2e0 zenon_H314 zenon_H30d zenon_H311 zenon_H305 zenon_H318 zenon_H13b zenon_H195 zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H1f3 zenon_H1cd zenon_H1cc zenon_H19b zenon_H1e6 zenon_H1bd zenon_H1ec zenon_H244 zenon_H245 zenon_H1f7 zenon_H14e. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.35/51.53 apply (zenon_L132_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.35/51.53 apply (zenon_L574_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.35/51.53 apply (zenon_L518_); trivial. % 51.35/51.53 apply (zenon_L149_); trivial. % 51.35/51.53 (* end of lemma zenon_L575_ *) % 51.35/51.53 assert (zenon_L576_ : (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> ((op2 (e22) (e20)) = (e22)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H39a zenon_H7c zenon_H176 zenon_H349 zenon_H15e zenon_H13 zenon_H14. % 51.35/51.53 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))). % 51.35/51.53 intro zenon_D_pnotp. % 51.35/51.53 apply zenon_H39a. % 51.35/51.53 rewrite <- zenon_D_pnotp. % 51.35/51.53 exact zenon_H349. % 51.35/51.53 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H39b]. % 51.35/51.53 cut (((h4 (e12)) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H39c]. % 51.35/51.53 congruence. % 51.35/51.53 elim (classic ((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [ zenon_intro zenon_H39d | zenon_intro zenon_H39e ]. % 51.35/51.53 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10)))) = ((h4 (e12)) = (h4 (op1 (e12) (e10))))). % 51.35/51.53 intro zenon_D_pnotp. % 51.35/51.53 apply zenon_H39c. % 51.35/51.53 rewrite <- zenon_D_pnotp. % 51.35/51.53 exact zenon_H39d. % 51.35/51.53 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H39e]. % 51.35/51.53 cut (((h4 (op1 (e12) (e10))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H39f]. % 51.35/51.53 congruence. % 51.35/51.53 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 51.35/51.53 congruence. % 51.35/51.53 exact (zenon_H10d zenon_H7c). % 51.35/51.53 apply zenon_H39e. apply refl_equal. % 51.35/51.53 apply zenon_H39e. apply refl_equal. % 51.35/51.53 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H3a0 | zenon_intro zenon_H3a1 ]. % 51.35/51.53 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e12)) (h4 (e10))))). % 51.35/51.53 intro zenon_D_pnotp. % 51.35/51.53 apply zenon_H39b. % 51.35/51.53 rewrite <- zenon_D_pnotp. % 51.35/51.53 exact zenon_H3a0. % 51.35/51.53 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3a1]. % 51.35/51.53 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3a2]. % 51.35/51.53 congruence. % 51.35/51.53 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (h4 (e12)) (h4 (e10))) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))). % 51.35/51.53 intro zenon_D_pnotp. % 51.35/51.53 apply zenon_H3a2. % 51.35/51.53 rewrite <- zenon_D_pnotp. % 51.35/51.53 exact zenon_H176. % 51.35/51.53 cut (((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H37f]. % 51.35/51.53 cut (((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3a3]. % 51.35/51.53 congruence. % 51.35/51.53 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H3a0 | zenon_intro zenon_H3a1 ]. % 51.35/51.53 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))). % 51.35/51.53 intro zenon_D_pnotp. % 51.35/51.53 apply zenon_H3a3. % 51.35/51.53 rewrite <- zenon_D_pnotp. % 51.35/51.53 exact zenon_H3a0. % 51.35/51.53 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3a1]. % 51.35/51.53 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H3a4]. % 51.35/51.53 congruence. % 51.35/51.53 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 51.35/51.53 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.35/51.53 congruence. % 51.35/51.53 apply (zenon_L487_); trivial. % 51.35/51.53 apply (zenon_L1_); trivial. % 51.35/51.53 apply zenon_H3a1. apply refl_equal. % 51.35/51.53 apply zenon_H3a1. apply refl_equal. % 51.35/51.53 exact (zenon_H37f zenon_H15e). % 51.35/51.53 apply zenon_H3a1. apply refl_equal. % 51.35/51.53 apply zenon_H3a1. apply refl_equal. % 51.35/51.53 (* end of lemma zenon_L576_ *) % 51.35/51.53 assert (zenon_L577_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e20)) = (e22)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.35/51.53 do 0 intro. intros zenon_H32a zenon_Hfe zenon_H2b zenon_Ha2 zenon_H125 zenon_H2d1 zenon_H24 zenon_H2c9 zenon_H2be zenon_H2c5 zenon_H2e1 zenon_H14 zenon_H13 zenon_H15e zenon_H349 zenon_H176 zenon_H39a zenon_Hff zenon_Hf6 zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H72 zenon_H65 zenon_H2ce zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_H3d zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H2db zenon_H318 zenon_H23 zenon_Hfb zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.53 apply (zenon_L281_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.53 apply (zenon_L282_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.53 apply (zenon_L7_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.53 apply (zenon_L325_); trivial. % 51.35/51.53 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.53 apply (zenon_L576_); trivial. % 51.35/51.53 apply (zenon_L384_); trivial. % 51.35/51.53 (* end of lemma zenon_L577_ *) % 51.35/51.53 assert (zenon_L578_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((op2 (e22) (e20)) = (e22)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H13b zenon_H318 zenon_H2db zenon_H305 zenon_H311 zenon_H2ff zenon_H30d zenon_H314 zenon_H2e0 zenon_H2ce zenon_H2d4 zenon_H2d1 zenon_H39a zenon_H176 zenon_H349 zenon_H15e zenon_H13 zenon_H14 zenon_H2be zenon_H32a zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H327 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.35/51.54 apply (zenon_L577_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.35/51.54 apply (zenon_L426_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.35/51.54 apply (zenon_L577_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.54 apply (zenon_L7_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.54 apply (zenon_L281_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.54 apply (zenon_L282_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.54 apply (zenon_L7_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.54 apply (zenon_L99_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.54 apply (zenon_L576_); trivial. % 51.35/51.54 apply (zenon_L543_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.35/51.54 apply (zenon_L512_); trivial. % 51.35/51.54 apply (zenon_L82_); trivial. % 51.35/51.54 apply (zenon_L85_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.35/51.54 apply (zenon_L4_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.35/51.54 apply (zenon_L109_); trivial. % 51.35/51.54 apply (zenon_L47_); trivial. % 51.35/51.54 (* end of lemma zenon_L578_ *) % 51.35/51.54 assert (zenon_L579_ : ((h4 (e11)) = (op2 (e23) (e23))) -> ((op1 (e12) (e11)) = (e11)) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (h4 (op1 (e12) (e11))))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H2e7 zenon_H330 zenon_H14e zenon_H3a5. % 51.35/51.54 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H3a6 | zenon_intro zenon_H3a7 ]. % 51.35/51.54 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((e21) = (h4 (op1 (e12) (e11))))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3a5. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H3a6. % 51.35/51.54 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3a7]. % 51.35/51.54 cut (((h4 (op1 (e12) (e11))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3a8]. % 51.35/51.54 congruence. % 51.35/51.54 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e12) (e11))) = (e21))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3a8. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H2e7. % 51.35/51.54 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 51.35/51.54 cut (((h4 (e11)) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3a9]. % 51.35/51.54 congruence. % 51.35/51.54 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H3a6 | zenon_intro zenon_H3a7 ]. % 51.35/51.54 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((h4 (e11)) = (h4 (op1 (e12) (e11))))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3a9. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H3a6. % 51.35/51.54 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3a7]. % 51.35/51.54 cut (((h4 (op1 (e12) (e11))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3aa]. % 51.35/51.54 congruence. % 51.35/51.54 cut (((op1 (e12) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3ab]. % 51.35/51.54 congruence. % 51.35/51.54 exact (zenon_H3ab zenon_H330). % 51.35/51.54 apply zenon_H3a7. apply refl_equal. % 51.35/51.54 apply zenon_H3a7. apply refl_equal. % 51.35/51.54 apply zenon_H14f. apply sym_equal. exact zenon_H14e. % 51.35/51.54 apply zenon_H3a7. apply refl_equal. % 51.35/51.54 apply zenon_H3a7. apply refl_equal. % 51.35/51.54 (* end of lemma zenon_L579_ *) % 51.35/51.54 assert (zenon_L580_ : ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((op1 (e12) (e11)) = (e11)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H330 zenon_H3ad. % 51.35/51.54 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H3ae | zenon_intro zenon_H3af ]. % 51.35/51.54 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3ad. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H3ae. % 51.35/51.54 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3af]. % 51.35/51.54 cut (((op2 (h4 (e12)) (h4 (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3b0]. % 51.35/51.54 congruence. % 51.35/51.54 cut (((op2 (e22) (e21)) = (e21)) = ((op2 (h4 (e12)) (h4 (e11))) = (h4 (op1 (e12) (e11))))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3b0. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H3ac. % 51.35/51.54 cut (((e21) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3a5]. % 51.35/51.54 cut (((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3b1]. % 51.35/51.54 congruence. % 51.35/51.54 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H3ae | zenon_intro zenon_H3af ]. % 51.35/51.54 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3b1. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H3ae. % 51.35/51.54 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3af]. % 51.35/51.54 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H3b2]. % 51.35/51.54 congruence. % 51.35/51.54 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2e6]. % 51.35/51.54 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.35/51.54 congruence. % 51.35/51.54 apply (zenon_L487_); trivial. % 51.35/51.54 apply (zenon_L326_); trivial. % 51.35/51.54 apply zenon_H3af. apply refl_equal. % 51.35/51.54 apply zenon_H3af. apply refl_equal. % 51.35/51.54 apply (zenon_L579_); trivial. % 51.35/51.54 apply zenon_H3af. apply refl_equal. % 51.35/51.54 apply zenon_H3af. apply refl_equal. % 51.35/51.54 (* end of lemma zenon_L580_ *) % 51.35/51.54 assert (zenon_L581_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((op1 (e12) (e10)) = (e13)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e11) = (e13))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H33e zenon_He2 zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H3d zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_Hcf zenon_Hc2 zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H49 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H51 zenon_H65 zenon_Hde zenon_H8c zenon_Hbe zenon_H31e zenon_H2be zenon_Ha2 zenon_H72 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H2d1 zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L421_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L476_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 (* end of lemma zenon_L581_ *) % 51.35/51.54 assert (zenon_L582_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((e11) = (e12))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((e11) = (e13))) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op1 (e12) (e10)) = (e13)) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H327 zenon_H105 zenon_H10b zenon_H9e zenon_H2d1 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Ha2 zenon_H2be zenon_H31e zenon_Hde zenon_H65 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H49 zenon_H318 zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_Hfb zenon_H3b zenon_Hf6 zenon_H2e0 zenon_Hcf zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_Hea zenon_Hb0 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H30b zenon_H3d zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H3ad zenon_He2 zenon_H33e zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L421_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L451_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.54 apply (zenon_L299_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L75_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L470_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.35/51.54 apply (zenon_L39_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.35/51.54 apply (zenon_L581_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.35/51.54 apply (zenon_L41_); trivial. % 51.35/51.54 apply (zenon_L24_); trivial. % 51.35/51.54 (* end of lemma zenon_L582_ *) % 51.35/51.54 assert (zenon_L583_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((op1 (e12) (e10)) = (e13)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e11) = (e13))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H2e1 zenon_H33e zenon_He2 zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H3d zenon_H30b zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H7d zenon_Hcf zenon_H2e0 zenon_Hf6 zenon_H3b zenon_Hfb zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H318 zenon_H90 zenon_H42 zenon_Hda zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H65 zenon_Hde zenon_H31e zenon_H2be zenon_Ha2 zenon_H72 zenon_H2ce zenon_H33a zenon_H46 zenon_H2d1 zenon_H9e zenon_H10b zenon_H105 zenon_H327 zenon_H2ff zenon_H7c zenon_H49 zenon_H2c zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.35/51.54 apply (zenon_L281_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.35/51.54 apply (zenon_L582_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.35/51.54 apply (zenon_L332_); trivial. % 51.35/51.54 apply (zenon_L309_); trivial. % 51.35/51.54 (* end of lemma zenon_L583_ *) % 51.35/51.54 assert (zenon_L584_ : (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e11)) -> False). % 51.35/51.54 do 0 intro. intros zenon_H3b3 zenon_H19 zenon_H3b4. % 51.35/51.54 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e11)) = (op1 (e13) (e13)))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3b3. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H19. % 51.35/51.54 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 51.35/51.54 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3b5]. % 51.35/51.54 congruence. % 51.35/51.54 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H3b6 | zenon_intro zenon_H3b7 ]. % 51.35/51.54 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e11) = (op1 (e13) (e11)))). % 51.35/51.54 intro zenon_D_pnotp. % 51.35/51.54 apply zenon_H3b5. % 51.35/51.54 rewrite <- zenon_D_pnotp. % 51.35/51.54 exact zenon_H3b6. % 51.35/51.54 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3b7]. % 51.35/51.54 cut (((op1 (e13) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H3b8]. % 51.35/51.54 congruence. % 51.35/51.54 exact (zenon_H3b8 zenon_H3b4). % 51.35/51.54 apply zenon_H3b7. apply refl_equal. % 51.35/51.54 apply zenon_H3b7. apply refl_equal. % 51.35/51.54 apply zenon_H5c. apply refl_equal. % 51.35/51.54 (* end of lemma zenon_L584_ *) % 51.35/51.54 assert (zenon_L585_ : (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e12) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((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 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H2ff zenon_H2ba zenon_H2e1 zenon_H31e zenon_H2be zenon_Ha2 zenon_H305 zenon_Hb5 zenon_H72 zenon_H65 zenon_H66 zenon_H49 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H335 zenon_H90 zenon_H7d zenon_H2d1 zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H327 zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_H35 zenon_Hd3 zenon_H95 zenon_H41 zenon_Hea zenon_H9e zenon_He1 zenon_Hde zenon_Hda zenon_H3d zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.35/51.54 apply (zenon_L282_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.35/51.54 apply (zenon_L333_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.35/51.54 apply (zenon_L334_); trivial. % 51.35/51.54 apply (zenon_L449_); trivial. % 51.35/51.54 (* end of lemma zenon_L585_ *) % 51.35/51.54 assert (zenon_L586_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H31e zenon_H2be zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H2ff zenon_H2ba zenon_H2e1 zenon_H305 zenon_Hb5 zenon_H4b zenon_H8c zenon_H2d1 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H335 zenon_H46 zenon_H2c6 zenon_H7c zenon_H33a zenon_H2ce zenon_H72 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.35/51.54 apply (zenon_L282_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.35/51.54 apply (zenon_L333_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.35/51.54 apply (zenon_L334_); trivial. % 51.35/51.54 apply (zenon_L468_); trivial. % 51.35/51.54 (* end of lemma zenon_L586_ *) % 51.35/51.54 assert (zenon_L587_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((e10) = (e11))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H33e zenon_H10b zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H3d zenon_Hb0 zenon_Ha3 zenon_Ha2 zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H72 zenon_H2ce zenon_H33a zenon_H7c zenon_H2c6 zenon_H46 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H2d1 zenon_H8c zenon_H4b zenon_Hb5 zenon_H305 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H2be zenon_H31e zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L75_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L586_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 (* end of lemma zenon_L587_ *) % 51.35/51.54 assert (zenon_L588_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e10) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H33e zenon_H10b zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H8c zenon_H2d1 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H46 zenon_H2c6 zenon_H1c zenon_H7c zenon_H2c zenon_H33a zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H51 zenon_H305 zenon_Ha2 zenon_H2be zenon_H31e zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L75_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L475_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 (* end of lemma zenon_L588_ *) % 51.35/51.54 assert (zenon_L589_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e10) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e11)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_Hf8 zenon_H327 zenon_Hcf zenon_Hd3 zenon_Hea zenon_He1 zenon_Hde zenon_Hda zenon_H45 zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb5 zenon_H4b zenon_Haf zenon_Hab zenon_H95 zenon_Hb0 zenon_H3d zenon_H33e zenon_H10b zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H8c zenon_H2d1 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H46 zenon_H2c6 zenon_H1c zenon_H7c zenon_H2c zenon_H33a zenon_H2ce zenon_H49 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H305 zenon_Ha2 zenon_H2be zenon_H31e zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L75_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L585_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.54 apply (zenon_L299_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.54 apply (zenon_L587_); trivial. % 51.35/51.54 apply (zenon_L588_); trivial. % 51.35/51.54 (* end of lemma zenon_L589_ *) % 51.35/51.54 assert (zenon_L590_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H33e zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H8c zenon_H1c zenon_Hc2 zenon_Hcf zenon_H2ce zenon_H46 zenon_H11a zenon_H65 zenon_H72 zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_Hb8 zenon_Hc8 zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L421_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L558_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 (* end of lemma zenon_L590_ *) % 51.35/51.54 assert (zenon_L591_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H19 zenon_H3d zenon_Hcb zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H1c zenon_H8c zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H11a zenon_H2c9 zenon_H54 zenon_H65 zenon_H72 zenon_H49 zenon_H90 zenon_Hda zenon_Hd3 zenon_Hde zenon_H45 zenon_H46 zenon_H34 zenon_Hf8 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H95 zenon_Hab zenon_H2c zenon_Haf zenon_H4b zenon_Hb5 zenon_H35 zenon_Hcf zenon_H50 zenon_H42. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.54 apply (zenon_L86_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.54 apply (zenon_L13_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.54 apply (zenon_L505_); trivial. % 51.35/51.54 apply (zenon_L17_); trivial. % 51.35/51.54 (* end of lemma zenon_L591_ *) % 51.35/51.54 assert (zenon_L592_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H8c zenon_H19 zenon_H11a zenon_H2c9 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H42 zenon_H49 zenon_H90 zenon_Hda zenon_Hd3 zenon_Hde zenon_H45 zenon_H46 zenon_H34 zenon_Hf8 zenon_H3d zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H95 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H4b zenon_Hb5 zenon_Hbe zenon_H35. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.35/51.54 apply (zenon_L281_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.35/51.54 apply (zenon_L284_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.35/51.54 apply (zenon_L503_); trivial. % 51.35/51.54 apply (zenon_L308_); trivial. % 51.35/51.54 (* end of lemma zenon_L592_ *) % 51.35/51.54 assert (zenon_L593_ : (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H35 zenon_Hbe zenon_Hb5 zenon_H4b zenon_Haf zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H3d zenon_Hf8 zenon_H34 zenon_H46 zenon_H45 zenon_Hde zenon_H90 zenon_H42 zenon_H72 zenon_H65 zenon_H66 zenon_H54 zenon_H2c9 zenon_H11a zenon_H19 zenon_H8c zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.35/51.54 apply (zenon_L592_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.35/51.54 apply (zenon_L34_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.35/51.54 apply (zenon_L45_); trivial. % 51.35/51.54 apply (zenon_L46_); trivial. % 51.35/51.54 (* end of lemma zenon_L593_ *) % 51.35/51.54 assert (zenon_L594_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.54 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H11a zenon_H2c9 zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H42 zenon_H90 zenon_Hde zenon_H45 zenon_H46 zenon_H34 zenon_Hf8 zenon_H3d zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H95 zenon_Haf zenon_H4b zenon_Hb5 zenon_H35 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.35/51.54 apply (zenon_L39_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.35/51.54 apply (zenon_L593_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.35/51.54 apply (zenon_L41_); trivial. % 51.35/51.54 apply (zenon_L24_); trivial. % 51.35/51.54 (* end of lemma zenon_L594_ *) % 51.35/51.54 assert (zenon_L595_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((e12) = (e13))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e10) = (e11))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> (~((e10) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H33e zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hfe zenon_H2b zenon_H2c9 zenon_Haf zenon_Ha2 zenon_Hde zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H10b zenon_Hff zenon_H23 zenon_Hc2 zenon_Hcf zenon_H10e zenon_He1 zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb0 zenon_Hea zenon_H95 zenon_Hb5 zenon_Hf8 zenon_H3d zenon_H4b zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H8c zenon_H2ce zenon_H46 zenon_H11a zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H51 zenon_H42 zenon_H49 zenon_H35 zenon_H90 zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L512_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L556_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 (* end of lemma zenon_L595_ *) % 51.35/51.54 assert (zenon_L596_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((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 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H90 zenon_H49 zenon_H72 zenon_H65 zenon_H66 zenon_H11a zenon_H46 zenon_H2ce zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H3ad zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H10e zenon_H23 zenon_Hff zenon_H10b zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_Ha2 zenon_H2c9 zenon_H2b zenon_Hfe zenon_H33e zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H327 zenon_Hb0 zenon_Hc8 zenon_Hb8 zenon_H42 zenon_H4b zenon_Hcf zenon_Hc2 zenon_H8c zenon_H35 zenon_Hbe zenon_Hd3 zenon_H95 zenon_H41 zenon_Hea zenon_H9e zenon_He1 zenon_Hde zenon_Hda zenon_H3d zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.35/51.54 apply (zenon_L15_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.35/51.54 apply (zenon_L595_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.35/51.54 apply (zenon_L437_); trivial. % 51.35/51.54 apply (zenon_L37_); trivial. % 51.35/51.54 (* end of lemma zenon_L596_ *) % 51.35/51.54 assert (zenon_L597_ : (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H2ce zenon_H46 zenon_H11a zenon_Ha3 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H30b zenon_H2c9 zenon_H10b zenon_H33e zenon_Hc2 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H131 zenon_Hbe zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hcb zenon_Hde zenon_H8c zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H2db zenon_H23 zenon_H24 zenon_H324 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H62 zenon_H3d zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.35/51.54 apply (zenon_L461_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.35/51.54 apply (zenon_L42_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.35/51.54 apply (zenon_L394_); trivial. % 51.35/51.54 apply (zenon_L37_); trivial. % 51.35/51.54 (* end of lemma zenon_L597_ *) % 51.35/51.54 assert (zenon_L598_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H33e zenon_H10b zenon_H7c zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H3d zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H8c zenon_Hbe zenon_H72 zenon_H65 zenon_H11a zenon_H46 zenon_H2ce zenon_Hcf zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L75_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L557_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 (* end of lemma zenon_L598_ *) % 51.35/51.54 assert (zenon_L599_ : (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H3b9 zenon_Hfb zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_Hf6 zenon_H113 zenon_H2e0 zenon_H10e zenon_Hff zenon_H9e zenon_Hcf zenon_H2ce zenon_H46 zenon_H11a zenon_H65 zenon_H72 zenon_Hbe zenon_H8c zenon_He1 zenon_H54 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H7c zenon_H10b zenon_H33e zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H324 zenon_H24 zenon_H23 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hd3 zenon_Hde zenon_Hcb zenon_H12c zenon_H128 zenon_H108 zenon_H131 zenon_H95 zenon_Ha2 zenon_Hb0 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H2c9 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H45 zenon_Hf8 zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H3b3 zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H104 | zenon_intro zenon_H3ba ]. % 51.35/51.54 apply (zenon_L406_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H3ba); [ zenon_intro zenon_H30b | zenon_intro zenon_H3bb ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.54 apply (zenon_L328_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.54 apply (zenon_L13_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.35/51.54 apply (zenon_L47_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.35/51.54 apply (zenon_L288_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.35/51.54 apply (zenon_L597_); trivial. % 51.35/51.54 apply (zenon_L24_); trivial. % 51.35/51.54 apply (zenon_L598_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H3bb); [ zenon_intro zenon_H330 | zenon_intro zenon_H3b4 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_L584_); trivial. % 51.35/51.54 (* end of lemma zenon_L599_ *) % 51.35/51.54 assert (zenon_L600_ : (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((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) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H3b3 zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H3ad zenon_Hf8 zenon_H45 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H2c9 zenon_Hb8 zenon_Hc8 zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H95 zenon_H131 zenon_H108 zenon_H128 zenon_H12c zenon_Hcb zenon_Hde zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H2db zenon_H23 zenon_H24 zenon_H324 zenon_Hab zenon_H2c zenon_Haf zenon_H33e zenon_H10b zenon_H7c zenon_H3d zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H72 zenon_H65 zenon_H11a zenon_H46 zenon_H2ce zenon_Hcf zenon_H9e zenon_Hff zenon_H10e zenon_H2e0 zenon_H113 zenon_Hf6 zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_Hfb zenon_H3b9 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.35/51.54 apply (zenon_L39_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.35/51.54 apply (zenon_L599_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.35/51.54 apply (zenon_L41_); trivial. % 51.35/51.54 apply (zenon_L24_); trivial. % 51.35/51.54 (* end of lemma zenon_L600_ *) % 51.35/51.54 assert (zenon_L601_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H33e zenon_Hfe zenon_H2b zenon_H2c9 zenon_H72 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H10b zenon_Hff zenon_H23 zenon_H10e zenon_He1 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H45 zenon_Hea zenon_Hf8 zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H3d zenon_Hb0 zenon_Ha3 zenon_Ha2 zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H90 zenon_H35 zenon_Hc2 zenon_Hde zenon_Hcb zenon_H42 zenon_Hb5 zenon_H4b zenon_Hcf zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H11a zenon_H46 zenon_H2ce zenon_H8c zenon_H9e zenon_H19. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.35/51.54 apply (zenon_L512_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.35/51.54 apply (zenon_L580_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.35/51.54 apply (zenon_L460_); trivial. % 51.35/51.54 apply (zenon_L452_); trivial. % 51.35/51.54 (* end of lemma zenon_L601_ *) % 51.35/51.54 assert (zenon_L602_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.35/51.54 do 0 intro. intros zenon_Hff zenon_He8 zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H108 zenon_H23 zenon_Hfb zenon_H3d zenon_H11a zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.54 apply (zenon_L317_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.54 apply (zenon_L407_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.54 apply (zenon_L427_); trivial. % 51.35/51.54 apply (zenon_L335_); trivial. % 51.35/51.54 (* end of lemma zenon_L602_ *) % 51.35/51.54 assert (zenon_L603_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((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 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.35/51.54 do 0 intro. intros zenon_H32a zenon_H2be zenon_H3b9 zenon_H117 zenon_H105 zenon_Hf6 zenon_H113 zenon_H2e0 zenon_H324 zenon_H24 zenon_H2db zenon_H12c zenon_H128 zenon_H131 zenon_H2ff zenon_H327 zenon_H3b3 zenon_H33e zenon_Hfe zenon_H2b zenon_H2c9 zenon_Haf zenon_Ha2 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H10b zenon_H10e zenon_H95 zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H2ce zenon_H65 zenon_H72 zenon_Hff zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H108 zenon_H23 zenon_Hfb zenon_H3d zenon_H11a zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.35/51.54 apply (zenon_L7_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.35/51.54 apply (zenon_L281_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.35/51.54 apply (zenon_L282_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.35/51.54 apply (zenon_L7_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.35/51.54 apply (zenon_L99_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.35/51.54 apply (zenon_L317_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.35/51.54 apply (zenon_L317_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.35/51.54 apply (zenon_L328_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.35/51.54 apply (zenon_L600_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.35/51.54 apply (zenon_L328_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.35/51.54 apply (zenon_L13_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.35/51.54 apply (zenon_L601_); trivial. % 51.35/51.54 apply (zenon_L595_); trivial. % 51.35/51.54 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.35/51.54 apply (zenon_L427_); trivial. % 51.35/51.54 apply (zenon_L15_); trivial. % 51.35/51.54 apply (zenon_L602_); trivial. % 51.35/51.54 (* end of lemma zenon_L603_ *) % 51.35/51.54 assert (zenon_L604_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H318 zenon_H11a zenon_Hfb zenon_H23 zenon_Hff zenon_H72 zenon_H65 zenon_H2ce zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H3ad zenon_H10b zenon_H2e1 zenon_H2c5 zenon_Ha2 zenon_H2c9 zenon_H2b zenon_Hfe zenon_H33e zenon_H3b3 zenon_H327 zenon_H131 zenon_H128 zenon_H12c zenon_H2db zenon_H24 zenon_H324 zenon_H2e0 zenon_H113 zenon_Hf6 zenon_H105 zenon_H117 zenon_H3b9 zenon_H2be zenon_H32a zenon_Hd3 zenon_H1c zenon_H2c zenon_H3d zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H305 zenon_Hc8 zenon_Hb8 zenon_He8 zenon_H4b zenon_Hcf zenon_H95 zenon_H10e zenon_Hb5 zenon_Hde zenon_H123 zenon_H311 zenon_Haf zenon_Hab zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_Hb0 zenon_Hc2 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hf8 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_H8c zenon_H126 zenon_H54 zenon_H19. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.55 apply (zenon_L603_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.55 apply (zenon_L358_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.55 apply (zenon_L359_); trivial. % 51.40/51.55 apply (zenon_L33_); trivial. % 51.40/51.55 (* end of lemma zenon_L604_ *) % 51.40/51.55 assert (zenon_L605_ : ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((e10) = (e11))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((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 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e11) = (e12))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H46 zenon_Hbe zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H31b zenon_H126 zenon_H8c zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_Hf8 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc2 zenon_H311 zenon_H123 zenon_Hb5 zenon_H10e zenon_H95 zenon_Hcf zenon_H4b zenon_Hb8 zenon_Hc8 zenon_H305 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H32a zenon_H2be zenon_H3b9 zenon_H117 zenon_H105 zenon_Hf6 zenon_H113 zenon_H2e0 zenon_H324 zenon_H24 zenon_H2db zenon_H12c zenon_H128 zenon_H131 zenon_H327 zenon_H3b3 zenon_H33e zenon_Hfe zenon_H2b zenon_H2c9 zenon_Ha2 zenon_H2c5 zenon_H2e1 zenon_H10b zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H2ce zenon_H72 zenon_Hff zenon_H23 zenon_Hfb zenon_H11a zenon_H318 zenon_Hde zenon_H65 zenon_H62 zenon_Hd3 zenon_H3d zenon_H19. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.55 apply (zenon_L596_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.55 apply (zenon_L40_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.55 apply (zenon_L335_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31b); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H31c ]. % 51.40/51.55 apply (zenon_L39_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31c); [ zenon_intro zenon_H114 | zenon_intro zenon_H31d ]. % 51.40/51.55 apply (zenon_L82_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_He8 | zenon_intro zenon_H66 ]. % 51.40/51.55 apply (zenon_L604_); trivial. % 51.40/51.55 apply (zenon_L363_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.55 apply (zenon_L355_); trivial. % 51.40/51.55 apply (zenon_L37_); trivial. % 51.40/51.55 apply (zenon_L37_); trivial. % 51.40/51.55 (* end of lemma zenon_L605_ *) % 51.40/51.55 assert (zenon_L606_ : ((op1 (e13) (e12)) = (e12)) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e10) (e11)) = (e13)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.55 do 0 intro. intros zenon_Hf1 zenon_H3d zenon_Hd3 zenon_H65 zenon_Hde zenon_H318 zenon_H11a zenon_Hfb zenon_H23 zenon_Hff zenon_H72 zenon_H2ce zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H3ad zenon_H10b zenon_H2e1 zenon_H2c5 zenon_Ha2 zenon_H2c9 zenon_H2b zenon_Hfe zenon_H33e zenon_H3b3 zenon_H327 zenon_H131 zenon_H128 zenon_H12c zenon_H2db zenon_H24 zenon_H324 zenon_H2e0 zenon_H113 zenon_Hf6 zenon_H105 zenon_H117 zenon_H3b9 zenon_H2be zenon_H32a zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H305 zenon_Hc8 zenon_Hb8 zenon_H4b zenon_Hcf zenon_H95 zenon_H10e zenon_Hb5 zenon_H123 zenon_H311 zenon_Hc2 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hf8 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_H126 zenon_H31b zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_Hb0 zenon_Hbe zenon_H46 zenon_H19 zenon_H8c. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.55 apply (zenon_L47_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.55 apply (zenon_L338_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.55 apply (zenon_L605_); trivial. % 51.40/51.55 apply (zenon_L24_); trivial. % 51.40/51.55 (* end of lemma zenon_L606_ *) % 51.40/51.55 assert (zenon_L607_ : (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H95 zenon_Hbe zenon_Hcf zenon_H327 zenon_H33e zenon_Hfe zenon_H2b zenon_H2c9 zenon_Ha2 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H10b zenon_Hff zenon_H23 zenon_H10e zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hf8 zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H2ce zenon_H46 zenon_H11a zenon_H65 zenon_H72 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_Hde zenon_H8c zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.55 apply (zenon_L596_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.55 apply (zenon_L42_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.55 apply (zenon_L373_); trivial. % 51.40/51.55 apply (zenon_L37_); trivial. % 51.40/51.55 (* end of lemma zenon_L607_ *) % 51.40/51.55 assert (zenon_L608_ : (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.55 do 0 intro. intros zenon_Hea zenon_Hf8 zenon_H10e zenon_H23 zenon_Hff zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2b zenon_Hfe zenon_H45 zenon_Hc8 zenon_Hb8 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_Hde zenon_Hc2 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H95 zenon_Ha2 zenon_Hb0 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H30b zenon_H2c9 zenon_Hcb zenon_H33e zenon_H10b zenon_H7c zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H3d zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H8c zenon_Hbe zenon_H72 zenon_H65 zenon_H11a zenon_H46 zenon_H2ce zenon_Hcf zenon_H9e zenon_H19. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.55 apply (zenon_L607_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.55 apply (zenon_L13_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.55 apply (zenon_L463_); trivial. % 51.40/51.55 apply (zenon_L598_); trivial. % 51.40/51.55 (* end of lemma zenon_L608_ *) % 51.40/51.55 assert (zenon_L609_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((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) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e10) = (e11))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H318 zenon_H3b3 zenon_H2ff zenon_H131 zenon_H128 zenon_H12c zenon_H2db zenon_H24 zenon_H324 zenon_H2e0 zenon_H113 zenon_Hf6 zenon_H105 zenon_H117 zenon_Hfb zenon_H3b9 zenon_H9e zenon_Hcf zenon_H2ce zenon_H46 zenon_H11a zenon_H65 zenon_H72 zenon_Hbe zenon_He1 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H3ad zenon_H7c zenon_H10b zenon_H33e zenon_Hcb zenon_H2c9 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_Hb0 zenon_Ha2 zenon_H95 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_Hc2 zenon_Hde zenon_Hb5 zenon_H4b zenon_Hd3 zenon_Hb8 zenon_Hc8 zenon_H45 zenon_Hfe zenon_H2b zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_Hff zenon_H23 zenon_H10e zenon_Hf8 zenon_Hea zenon_H8c zenon_H126 zenon_H54 zenon_H19. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.55 apply (zenon_L599_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.55 apply (zenon_L608_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.55 apply (zenon_L359_); trivial. % 51.40/51.55 apply (zenon_L33_); trivial. % 51.40/51.55 (* end of lemma zenon_L609_ *) % 51.40/51.55 assert (zenon_L610_ : ((op1 (e13) (e11)) = (e10)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((e12) = (e13))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((e10) = (e11))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.55 do 0 intro. intros zenon_Hbe zenon_H327 zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H33e zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hfe zenon_H2b zenon_H2c9 zenon_Haf zenon_Ha2 zenon_Hde zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H10b zenon_Hff zenon_H23 zenon_Hc2 zenon_Hcf zenon_H10e zenon_He1 zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb0 zenon_Hea zenon_H95 zenon_Hb5 zenon_Hf8 zenon_H3d zenon_H4b zenon_H3ad zenon_H14e zenon_H2e7 zenon_H15e zenon_H349 zenon_H3ac zenon_H8c zenon_H2ce zenon_H46 zenon_H11a zenon_H54 zenon_H66 zenon_H65 zenon_H72 zenon_H42 zenon_H49 zenon_H35 zenon_H90 zenon_H9e zenon_H19. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.55 apply (zenon_L596_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.55 apply (zenon_L299_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.55 apply (zenon_L601_); trivial. % 51.40/51.55 apply (zenon_L595_); trivial. % 51.40/51.55 (* end of lemma zenon_L610_ *) % 51.40/51.55 assert (zenon_L611_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H13b zenon_H318 zenon_H305 zenon_H311 zenon_H30d zenon_H314 zenon_H2d4 zenon_H31e zenon_H31b zenon_H2d1 zenon_H2ce zenon_H3ac zenon_H349 zenon_H15e zenon_H2e7 zenon_H14e zenon_H3ad zenon_H33e zenon_H3b3 zenon_H327 zenon_H2ff zenon_H2db zenon_H324 zenon_H2e0 zenon_H3b9 zenon_H2be zenon_H32a zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H341 zenon_H33a zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.40/51.55 apply (zenon_L7_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.40/51.55 apply (zenon_L281_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.40/51.55 apply (zenon_L282_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.55 apply (zenon_L7_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.55 apply (zenon_L325_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.55 apply (zenon_L11_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.55 apply (zenon_L11_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.55 apply (zenon_L12_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.55 apply (zenon_L283_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.55 apply (zenon_L328_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.40/51.55 apply (zenon_L86_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.40/51.55 apply (zenon_L75_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.40/51.55 apply (zenon_L580_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.40/51.55 apply (zenon_L451_); trivial. % 51.40/51.55 apply (zenon_L452_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.40/51.55 apply (zenon_L454_); trivial. % 51.40/51.55 apply (zenon_L34_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.55 apply (zenon_L359_); trivial. % 51.40/51.55 apply (zenon_L33_); trivial. % 51.40/51.55 apply (zenon_L369_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H104 | zenon_intro zenon_H3ba ]. % 51.40/51.55 apply (zenon_L385_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H3ba); [ zenon_intro zenon_H30b | zenon_intro zenon_H3bb ]. % 51.40/51.55 apply (zenon_L583_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H3bb); [ zenon_intro zenon_H330 | zenon_intro zenon_H3b4 ]. % 51.40/51.55 apply (zenon_L580_); trivial. % 51.40/51.55 apply (zenon_L584_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.40/51.55 apply (zenon_L281_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.40/51.55 apply (zenon_L589_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.40/51.55 apply (zenon_L332_); trivial. % 51.40/51.55 apply (zenon_L309_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.55 apply (zenon_L378_); trivial. % 51.40/51.55 apply (zenon_L15_); trivial. % 51.40/51.55 apply (zenon_L384_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.40/51.55 apply (zenon_L426_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.40/51.55 apply (zenon_L7_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.40/51.55 apply (zenon_L281_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.40/51.55 apply (zenon_L282_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.55 apply (zenon_L7_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.55 apply (zenon_L317_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.55 apply (zenon_L317_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.55 apply (zenon_L86_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.55 apply (zenon_L9_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.55 apply (zenon_L283_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.40/51.55 apply (zenon_L281_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.40/51.55 apply (zenon_L284_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.55 apply (zenon_L86_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.55 apply (zenon_L13_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.55 apply (zenon_L298_); trivial. % 51.40/51.55 apply (zenon_L590_); trivial. % 51.40/51.55 apply (zenon_L309_); trivial. % 51.40/51.55 apply (zenon_L591_); trivial. % 51.40/51.55 apply (zenon_L594_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.55 apply (zenon_L427_); trivial. % 51.40/51.55 apply (zenon_L15_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.55 apply (zenon_L11_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.55 apply (zenon_L11_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.55 apply (zenon_L12_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.55 apply (zenon_L283_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.40/51.55 apply (zenon_L282_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.40/51.55 apply (zenon_L333_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.40/51.55 apply (zenon_L334_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.55 apply (zenon_L39_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.55 apply (zenon_L606_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.55 apply (zenon_L41_); trivial. % 51.40/51.55 apply (zenon_L24_); trivial. % 51.40/51.55 apply (zenon_L377_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.55 apply (zenon_L600_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.55 apply (zenon_L12_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.55 apply (zenon_L13_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.55 apply (zenon_L464_); trivial. % 51.40/51.55 apply (zenon_L590_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.55 apply (zenon_L482_); trivial. % 51.40/51.55 apply (zenon_L33_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.55 apply (zenon_L283_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.55 apply (zenon_L39_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.55 apply (zenon_L609_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.55 apply (zenon_L41_); trivial. % 51.40/51.55 apply (zenon_L24_); trivial. % 51.40/51.55 apply (zenon_L377_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.55 apply (zenon_L39_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.55 apply (zenon_L610_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.55 apply (zenon_L41_); trivial. % 51.40/51.55 apply (zenon_L24_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.55 apply (zenon_L427_); trivial. % 51.40/51.55 apply (zenon_L335_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.55 apply (zenon_L317_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.55 apply (zenon_L317_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.55 apply (zenon_L71_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.55 apply (zenon_L283_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.55 apply (zenon_L604_); trivial. % 51.40/51.55 apply (zenon_L360_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.55 apply (zenon_L352_); trivial. % 51.40/51.55 apply (zenon_L57_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.55 apply (zenon_L383_); trivial. % 51.40/51.55 apply (zenon_L15_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.40/51.55 apply (zenon_L603_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.40/51.55 apply (zenon_L512_); trivial. % 51.40/51.55 apply (zenon_L82_); trivial. % 51.40/51.55 apply (zenon_L85_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.40/51.55 apply (zenon_L4_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.40/51.55 apply (zenon_L109_); trivial. % 51.40/51.55 apply (zenon_L47_); trivial. % 51.40/51.55 (* end of lemma zenon_L611_ *) % 51.40/51.55 assert (zenon_L612_ : ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H176 zenon_H156 zenon_H1b1 zenon_H1bd zenon_H1bc zenon_H1cd zenon_H1c9 zenon_H1cc zenon_H14e zenon_H244 zenon_H245. % 51.40/51.55 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.40/51.55 apply (zenon_L133_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.40/51.55 apply (zenon_L134_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.40/51.55 apply (zenon_L136_); trivial. % 51.40/51.55 apply (zenon_L172_); trivial. % 51.40/51.55 (* end of lemma zenon_L612_ *) % 51.40/51.55 assert (zenon_L613_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H1c9 zenon_H1cd zenon_H1b1 zenon_H156 zenon_H176 zenon_H245 zenon_H244 zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H175 zenon_H15e zenon_H14 zenon_H187 zenon_H19b zenon_H1cc zenon_H18e zenon_H195 zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H1fd zenon_H21f zenon_H1f7 zenon_H14e. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.40/51.55 apply (zenon_L132_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.40/51.55 apply (zenon_L612_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.40/51.55 apply (zenon_L180_); trivial. % 51.40/51.55 apply (zenon_L149_); trivial. % 51.40/51.55 (* end of lemma zenon_L613_ *) % 51.40/51.55 assert (zenon_L614_ : (~((op2 (e23) (e23)) = (op2 (op2 (e20) (e21)) (op2 (e20) (e21))))) -> ((op2 (e20) (e21)) = (e23)) -> False). % 51.40/51.55 do 0 intro. intros zenon_H3bc zenon_H244. % 51.40/51.55 cut (((e23) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H249]. % 51.40/51.55 cut (((e23) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H249]. % 51.40/51.55 congruence. % 51.40/51.55 apply zenon_H249. apply sym_equal. exact zenon_H244. % 51.40/51.55 apply zenon_H249. apply sym_equal. exact zenon_H244. % 51.40/51.55 (* end of lemma zenon_L614_ *) % 51.40/51.55 assert (zenon_L615_ : (~((op2 (e23) (e23)) = (op2 (e20) (e22)))) -> ((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e21)) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e20) (e22)) = (e21)) -> False). % 51.40/51.55 do 0 intro. intros zenon_H3bd zenon_H1b5 zenon_H244 zenon_H293. % 51.40/51.55 cut (((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (e21)) = ((op2 (e23) (e23)) = (op2 (e20) (e22)))). % 51.40/51.55 intro zenon_D_pnotp. % 51.40/51.55 apply zenon_H3bd. % 51.40/51.55 rewrite <- zenon_D_pnotp. % 51.40/51.55 exact zenon_H1b5. % 51.40/51.55 cut (((e21) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H36c]. % 51.40/51.55 cut (((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3be]. % 51.40/51.55 congruence. % 51.40/51.55 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H196 | zenon_intro zenon_H197 ]. % 51.40/51.55 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (op2 (e20) (e21)) (op2 (e20) (e21))) = (op2 (e23) (e23)))). % 51.40/51.55 intro zenon_D_pnotp. % 51.40/51.55 apply zenon_H3be. % 51.40/51.55 rewrite <- zenon_D_pnotp. % 51.40/51.55 exact zenon_H196. % 51.40/51.55 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 51.40/51.55 cut (((op2 (e23) (e23)) = (op2 (op2 (e20) (e21)) (op2 (e20) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H3bc]. % 51.40/51.55 congruence. % 51.40/51.55 apply (zenon_L614_); trivial. % 51.40/51.55 apply zenon_H197. apply refl_equal. % 51.40/51.55 apply zenon_H197. apply refl_equal. % 51.40/51.55 apply zenon_H36c. apply sym_equal. exact zenon_H293. % 51.40/51.55 (* end of lemma zenon_L615_ *) % 51.40/51.55 assert (zenon_L616_ : (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e22) (e22)) = (e21)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H2b7 zenon_H293 zenon_H3bf zenon_H1bd zenon_H1bc zenon_H1cd zenon_H1c9 zenon_H1cc zenon_H14e zenon_H244 zenon_H245. % 51.40/51.55 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.40/51.55 apply (zenon_and_s _ _ zenon_H1b0). zenon_intro zenon_H1b3. zenon_intro zenon_H1b2. % 51.40/51.55 apply (zenon_and_s _ _ zenon_H1b2). zenon_intro zenon_H1b5. zenon_intro zenon_H1b4. % 51.40/51.55 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.40/51.55 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 51.40/51.55 intro zenon_D_pnotp. % 51.40/51.55 apply zenon_H2b7. % 51.40/51.55 rewrite <- zenon_D_pnotp. % 51.40/51.55 exact zenon_H1a0. % 51.40/51.55 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.40/51.55 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b8]. % 51.40/51.55 congruence. % 51.40/51.55 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 51.40/51.55 intro zenon_D_pnotp. % 51.40/51.55 apply zenon_H2b8. % 51.40/51.55 rewrite <- zenon_D_pnotp. % 51.40/51.55 exact zenon_H14e. % 51.40/51.55 cut (((op2 (e23) (e23)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3bd]. % 51.40/51.55 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3c0]. % 51.40/51.55 congruence. % 51.40/51.55 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H1a0 | zenon_intro zenon_H1a1 ]. % 51.40/51.55 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e21) = (op2 (e22) (e22)))). % 51.40/51.55 intro zenon_D_pnotp. % 51.40/51.55 apply zenon_H3c0. % 51.40/51.55 rewrite <- zenon_D_pnotp. % 51.40/51.55 exact zenon_H1a0. % 51.40/51.55 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 51.40/51.55 cut (((op2 (e22) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3c1]. % 51.40/51.55 congruence. % 51.40/51.55 exact (zenon_H3c1 zenon_H3bf). % 51.40/51.55 apply zenon_H1a1. apply refl_equal. % 51.40/51.55 apply zenon_H1a1. apply refl_equal. % 51.40/51.55 apply (zenon_L615_); trivial. % 51.40/51.55 apply zenon_H1a1. apply refl_equal. % 51.40/51.55 apply zenon_H1a1. apply refl_equal. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.40/51.55 apply (zenon_L134_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.40/51.55 apply (zenon_L136_); trivial. % 51.40/51.55 apply (zenon_L172_); trivial. % 51.40/51.55 (* end of lemma zenon_L616_ *) % 51.40/51.55 assert (zenon_L617_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e21)) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.55 do 0 intro. intros zenon_H22f zenon_H16f zenon_H175 zenon_H205 zenon_H245 zenon_H244 zenon_H1cc zenon_H1cd zenon_H1bc zenon_H1bd zenon_H3bf zenon_H293 zenon_H2b7 zenon_H14e zenon_H210. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.55 apply (zenon_L129_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.55 apply (zenon_L184_); trivial. % 51.40/51.55 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.55 apply (zenon_L616_); trivial. % 51.40/51.55 apply (zenon_L154_); trivial. % 51.40/51.55 (* end of lemma zenon_L617_ *) % 51.40/51.55 assert (zenon_L618_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e21)) -> ((op2 (e22) (e22)) = (e21)) -> ((op2 (e23) (e20)) = (e23)) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H1fa zenon_H1ac zenon_H210 zenon_H2b7 zenon_H293 zenon_H3bf zenon_H1cd zenon_H205 zenon_H16f zenon_H22f zenon_H245 zenon_H244 zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H175 zenon_H15e zenon_H14 zenon_H187 zenon_H19b zenon_H1cc zenon_H18e zenon_H195 zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H1fd zenon_H21f zenon_H1f7 zenon_H14e. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.40/51.56 apply (zenon_L132_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.40/51.56 apply (zenon_L617_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.40/51.56 apply (zenon_L180_); trivial. % 51.40/51.56 apply (zenon_L149_); trivial. % 51.40/51.56 (* end of lemma zenon_L618_ *) % 51.40/51.56 assert (zenon_L619_ : (((op2 (e20) (e22)) = (e20))\/(((op2 (e20) (e22)) = (e21))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e22)) = (e23))))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e22) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e21))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H3c2 zenon_H176 zenon_H1b1 zenon_H1c9 zenon_H244 zenon_H245 zenon_H1cd zenon_H3bf zenon_H168 zenon_H205 zenon_H1fa zenon_H210 zenon_H14 zenon_H209 zenon_H22f zenon_H18e zenon_H19b zenon_H195 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H1ac zenon_H24e zenon_H187 zenon_H1ec zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H21f zenon_H1f7 zenon_H14e. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3c2); [ zenon_intro zenon_H156 | zenon_intro zenon_H3c3 ]. % 51.40/51.56 apply (zenon_L613_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3c3); [ zenon_intro zenon_H293 | zenon_intro zenon_H3c4 ]. % 51.40/51.56 apply (zenon_L618_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3c4); [ zenon_intro zenon_H169 | zenon_intro zenon_H256 ]. % 51.40/51.56 apply (zenon_L118_); trivial. % 51.40/51.56 apply (zenon_L277_); trivial. % 51.40/51.56 (* end of lemma zenon_L619_ *) % 51.40/51.56 assert (zenon_L620_ : ((op2 (e23) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e21))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((op2 (e22) (e22)) = (e21)) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e22)) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e20) (e22)) = (e21))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e22)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H203 zenon_H14e zenon_H1f7 zenon_H21f zenon_H217 zenon_H21b zenon_H1f3 zenon_H2b7 zenon_H1ec zenon_H187 zenon_H24e zenon_H1ac zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H175 zenon_H19b zenon_H18e zenon_H22f zenon_H209 zenon_H210 zenon_H1fa zenon_H205 zenon_H168 zenon_H3bf zenon_H1cd zenon_H245 zenon_H244 zenon_H1c9 zenon_H1b1 zenon_H176 zenon_H3c2 zenon_H15e zenon_H14 zenon_H195. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.40/51.56 apply (zenon_L192_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.40/51.56 apply (zenon_L162_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.40/51.56 apply (zenon_L619_); trivial. % 51.40/51.56 apply (zenon_L126_); trivial. % 51.40/51.56 (* end of lemma zenon_L620_ *) % 51.40/51.56 assert (zenon_L621_ : (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((e21) = (e22))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((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))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e20) (e22)) = (e21))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e22)) = (e23))))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e23)) = (e20)) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H3c5 zenon_H288 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H33a zenon_H341 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H32a zenon_H2be zenon_H3b9 zenon_H2e0 zenon_H324 zenon_H2db zenon_H2ff zenon_H327 zenon_H3b3 zenon_H33e zenon_H3ad zenon_H2e7 zenon_H349 zenon_H2ce zenon_H2d1 zenon_H31b zenon_H31e zenon_H2d4 zenon_H314 zenon_H30d zenon_H311 zenon_H305 zenon_H318 zenon_H13b zenon_H195 zenon_H14 zenon_H15e zenon_H3c2 zenon_H176 zenon_H1b1 zenon_H1c9 zenon_H244 zenon_H245 zenon_H1cd zenon_H168 zenon_H205 zenon_H1fa zenon_H210 zenon_H209 zenon_H22f zenon_H18e zenon_H19b zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H1ac zenon_H24e zenon_H187 zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H217 zenon_H21f zenon_H1f7 zenon_H203 zenon_H1ec zenon_H14e. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3c5); [ zenon_intro zenon_H26e | zenon_intro zenon_H3c6 ]. % 51.40/51.56 apply (zenon_L223_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3c6); [ zenon_intro zenon_H3ac | zenon_intro zenon_H3c7 ]. % 51.40/51.56 apply (zenon_L611_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3c7); [ zenon_intro zenon_H3bf | zenon_intro zenon_H29a ]. % 51.40/51.56 apply (zenon_L620_); trivial. % 51.40/51.56 apply (zenon_L235_); trivial. % 51.40/51.56 (* end of lemma zenon_L621_ *) % 51.40/51.56 assert (zenon_L622_ : (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e22)) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e20) (e22)) = (e21))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e22)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e21) = (e22))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H1ec zenon_H203 zenon_H1f7 zenon_H21f zenon_H217 zenon_H21b zenon_H1f3 zenon_H2b7 zenon_H187 zenon_H24e zenon_H1ac zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H175 zenon_H19b zenon_H18e zenon_H22f zenon_H209 zenon_H1fa zenon_H205 zenon_H168 zenon_H1cd zenon_H245 zenon_H244 zenon_H1b1 zenon_H176 zenon_H3c2 zenon_H15e zenon_H14 zenon_H195 zenon_H13b zenon_H318 zenon_H305 zenon_H311 zenon_H30d zenon_H314 zenon_H2d4 zenon_H31e zenon_H31b zenon_H2d1 zenon_H2ce zenon_H349 zenon_H2e7 zenon_H3ad zenon_H33e zenon_H3b3 zenon_H327 zenon_H2ff zenon_H2db zenon_H324 zenon_H2e0 zenon_H3b9 zenon_H2be zenon_H32a zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H341 zenon_H33a zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H288 zenon_H3c5 zenon_H14e zenon_H210. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.56 apply (zenon_L129_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.56 apply (zenon_L243_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.56 apply (zenon_L621_); trivial. % 51.40/51.56 apply (zenon_L154_); trivial. % 51.40/51.56 (* end of lemma zenon_L622_ *) % 51.40/51.56 assert (zenon_L623_ : (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((e21) = (e22))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((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))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e20) (e22)) = (e21))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e22)) = (e23))))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H3c5 zenon_H288 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H33a zenon_H341 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H32a zenon_H2be zenon_H3b9 zenon_H2e0 zenon_H324 zenon_H2db zenon_H2ff zenon_H327 zenon_H3b3 zenon_H33e zenon_H3ad zenon_H2e7 zenon_H349 zenon_H2ce zenon_H2d1 zenon_H31b zenon_H31e zenon_H2d4 zenon_H314 zenon_H30d zenon_H311 zenon_H305 zenon_H318 zenon_H13b zenon_H195 zenon_H15e zenon_H3c2 zenon_H176 zenon_H1b1 zenon_H244 zenon_H245 zenon_H1cd zenon_H168 zenon_H205 zenon_H1fa zenon_H22f zenon_H18e zenon_H19b zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H1ac zenon_H24e zenon_H187 zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H217 zenon_H21f zenon_H1f7 zenon_H1ec zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.40/51.56 apply (zenon_L151_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.40/51.56 apply (zenon_L622_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.40/51.56 apply (zenon_L153_); trivial. % 51.40/51.56 apply (zenon_L154_); trivial. % 51.40/51.56 (* end of lemma zenon_L623_ *) % 51.40/51.56 assert (zenon_L624_ : (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((op2 (e22) (e21)) = (e23)) -> False). % 51.40/51.56 do 0 intro. intros zenon_H3c8 zenon_H244 zenon_H3c9. % 51.40/51.56 cut (((op2 (e20) (e21)) = (e23)) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))). % 51.40/51.56 intro zenon_D_pnotp. % 51.40/51.56 apply zenon_H3c8. % 51.40/51.56 rewrite <- zenon_D_pnotp. % 51.40/51.56 exact zenon_H244. % 51.40/51.56 cut (((e23) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H3ca]. % 51.40/51.56 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 51.40/51.56 congruence. % 51.40/51.56 apply zenon_H154. apply refl_equal. % 51.40/51.56 apply zenon_H3ca. apply sym_equal. exact zenon_H3c9. % 51.40/51.56 (* end of lemma zenon_L624_ *) % 51.40/51.56 assert (zenon_L625_ : ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((e23) = (op2 (h4 (e12)) (h4 (e12))))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H3cb zenon_H349 zenon_H15e zenon_H3cc. % 51.40/51.56 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H3cd | zenon_intro zenon_H3ce ]. % 51.40/51.56 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((e23) = (op2 (h4 (e12)) (h4 (e12))))). % 51.40/51.56 intro zenon_D_pnotp. % 51.40/51.56 apply zenon_H3cc. % 51.40/51.56 rewrite <- zenon_D_pnotp. % 51.40/51.56 exact zenon_H3cd. % 51.40/51.56 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3ce]. % 51.40/51.56 cut (((op2 (h4 (e12)) (h4 (e12))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H3cf]. % 51.40/51.56 congruence. % 51.40/51.56 cut (((op2 (e22) (e22)) = (e23)) = ((op2 (h4 (e12)) (h4 (e12))) = (e23))). % 51.40/51.56 intro zenon_D_pnotp. % 51.40/51.56 apply zenon_H3cf. % 51.40/51.56 rewrite <- zenon_D_pnotp. % 51.40/51.56 exact zenon_H3cb. % 51.40/51.56 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.40/51.56 cut (((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3d0]. % 51.40/51.56 congruence. % 51.40/51.56 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H3cd | zenon_intro zenon_H3ce ]. % 51.40/51.56 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))). % 51.40/51.56 intro zenon_D_pnotp. % 51.40/51.56 apply zenon_H3d0. % 51.40/51.56 rewrite <- zenon_D_pnotp. % 51.40/51.56 exact zenon_H3cd. % 51.40/51.56 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3ce]. % 51.40/51.56 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3d1]. % 51.40/51.56 congruence. % 51.40/51.56 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.40/51.56 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.40/51.56 congruence. % 51.40/51.56 apply (zenon_L487_); trivial. % 51.40/51.56 apply (zenon_L487_); trivial. % 51.40/51.56 apply zenon_H3ce. apply refl_equal. % 51.40/51.56 apply zenon_H3ce. apply refl_equal. % 51.40/51.56 apply zenon_H14c. apply refl_equal. % 51.40/51.56 apply zenon_H3ce. apply refl_equal. % 51.40/51.56 apply zenon_H3ce. apply refl_equal. % 51.40/51.56 (* end of lemma zenon_L625_ *) % 51.40/51.56 assert (zenon_L626_ : (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op1 (e12) (e12)) = (e13)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H3d2 zenon_H2ea zenon_H3d3 zenon_H3cb zenon_H349 zenon_H15e. % 51.40/51.56 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))). % 51.40/51.56 intro zenon_D_pnotp. % 51.40/51.56 apply zenon_H3d2. % 51.40/51.56 rewrite <- zenon_D_pnotp. % 51.40/51.56 exact zenon_H2ea. % 51.40/51.56 cut (((e23) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3cc]. % 51.40/51.56 cut (((h4 (e13)) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3d4]. % 51.40/51.56 congruence. % 51.40/51.56 elim (classic ((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [ zenon_intro zenon_H3d5 | zenon_intro zenon_H3d6 ]. % 51.40/51.56 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12)))) = ((h4 (e13)) = (h4 (op1 (e12) (e12))))). % 51.40/51.56 intro zenon_D_pnotp. % 51.40/51.56 apply zenon_H3d4. % 51.40/51.56 rewrite <- zenon_D_pnotp. % 51.40/51.56 exact zenon_H3d5. % 51.40/51.56 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3d6]. % 51.40/51.56 cut (((h4 (op1 (e12) (e12))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3d7]. % 51.40/51.56 congruence. % 51.40/51.56 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H3d8]. % 51.40/51.56 congruence. % 51.40/51.56 exact (zenon_H3d8 zenon_H3d3). % 51.40/51.56 apply zenon_H3d6. apply refl_equal. % 51.40/51.56 apply zenon_H3d6. apply refl_equal. % 51.40/51.56 apply (zenon_L625_); trivial. % 51.40/51.56 (* end of lemma zenon_L626_ *) % 51.40/51.56 assert (zenon_L627_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.40/51.56 do 0 intro. intros zenon_Hf8 zenon_H8c zenon_Hcf zenon_He1 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_H4b zenon_Hb5 zenon_H3d zenon_Hb8 zenon_Hc8 zenon_H46 zenon_H45 zenon_Hcb zenon_Hf0 zenon_He8 zenon_Hec zenon_H19 zenon_H1c zenon_Hc2 zenon_Hf3 zenon_H50 zenon_H42. % 51.40/51.56 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.56 apply (zenon_L360_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.56 apply (zenon_L13_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.56 apply (zenon_L65_); trivial. % 51.40/51.56 apply (zenon_L17_); trivial. % 51.40/51.56 (* end of lemma zenon_L627_ *) % 51.40/51.56 assert (zenon_L628_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.40/51.56 do 0 intro. intros zenon_Hfb zenon_H3b zenon_H49 zenon_H318 zenon_H3d9 zenon_H2db zenon_H2ce zenon_H65 zenon_H72 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_H2e0 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H90 zenon_H35 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_H46 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_He8 zenon_H4b. % 51.40/51.56 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.56 apply (zenon_L11_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.56 apply (zenon_L12_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.56 apply (zenon_L283_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.56 apply (zenon_L328_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H314); [ zenon_intro zenon_H7c | zenon_intro zenon_H315 ]. % 51.40/51.56 apply (zenon_L341_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H316 ]. % 51.40/51.56 apply (zenon_L353_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H304 | zenon_intro zenon_Hd2 ]. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.56 apply (zenon_L382_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.56 apply (zenon_L65_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.56 apply (zenon_L626_); trivial. % 51.40/51.56 apply (zenon_L379_); trivial. % 51.40/51.56 apply (zenon_L45_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.56 apply (zenon_L359_); trivial. % 51.40/51.56 apply (zenon_L33_); trivial. % 51.40/51.56 apply (zenon_L627_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.56 apply (zenon_L352_); trivial. % 51.40/51.56 apply (zenon_L57_); trivial. % 51.40/51.56 (* end of lemma zenon_L628_ *) % 51.40/51.56 assert (zenon_L629_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.40/51.56 do 0 intro. intros zenon_Hff zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_He8 zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H72 zenon_H65 zenon_H2ce zenon_H42 zenon_Hda zenon_H7d zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H2db zenon_H318 zenon_H23 zenon_Hfb zenon_H49 zenon_H4b. % 51.40/51.56 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.56 apply (zenon_L11_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.56 apply (zenon_L628_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.56 apply (zenon_L383_); trivial. % 51.40/51.56 apply (zenon_L15_); trivial. % 51.40/51.56 (* end of lemma zenon_L629_ *) % 51.40/51.56 assert (zenon_L630_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H327 zenon_Hfb zenon_H23 zenon_H318 zenon_H2db zenon_H305 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H2ff zenon_H30d zenon_H314 zenon_H2e0 zenon_H90 zenon_H54 zenon_H7d zenon_H2ce zenon_H65 zenon_H72 zenon_Hcf zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_Hb0 zenon_Hf8 zenon_H3d9 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Hff zenon_H8c zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H19 zenon_H3d zenon_H49 zenon_H95 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_He1 zenon_H42 zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_Hb5 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.56 apply (zenon_L629_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.56 apply (zenon_L309_); trivial. % 51.40/51.56 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.56 apply (zenon_L338_); trivial. % 51.40/51.56 apply (zenon_L46_); trivial. % 51.40/51.56 (* end of lemma zenon_L630_ *) % 51.40/51.56 assert (zenon_L631_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.56 do 0 intro. intros zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H46 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H3d zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H2e0 zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H72 zenon_H2ce zenon_H2db zenon_H3d9 zenon_H318 zenon_H49 zenon_H3b zenon_Hfb zenon_Hde zenon_Hcc zenon_H65 zenon_H62 zenon_H51 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H31b); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H31c ]. % 51.40/51.57 apply (zenon_L39_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H31c); [ zenon_intro zenon_H114 | zenon_intro zenon_H31d ]. % 51.40/51.57 apply (zenon_L82_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_He8 | zenon_intro zenon_H66 ]. % 51.40/51.57 apply (zenon_L628_); trivial. % 51.40/51.57 apply (zenon_L363_); trivial. % 51.40/51.57 (* end of lemma zenon_L631_ *) % 51.40/51.57 assert (zenon_L632_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H327 zenon_Hf6 zenon_H2b zenon_Hfe zenon_H10b zenon_H23 zenon_H2e1 zenon_Ha2 zenon_Hff zenon_H105 zenon_H117 zenon_H324 zenon_H24 zenon_H12c zenon_H128 zenon_H131 zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H3d zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H2e0 zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_Haf zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H72 zenon_H2ce zenon_H2db zenon_H3d9 zenon_H318 zenon_H49 zenon_H3b zenon_Hfb zenon_Hde zenon_Hcc zenon_H65 zenon_H62 zenon_H51 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H1d | zenon_intro zenon_H2d5 ]. % 51.40/51.57 apply (zenon_L4_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2d5); [ zenon_intro zenon_H104 | zenon_intro zenon_H2d6 ]. % 51.40/51.57 apply (zenon_L426_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2d6); [ zenon_intro zenon_H2bb | zenon_intro zenon_H46 ]. % 51.40/51.57 apply (zenon_L281_); trivial. % 51.40/51.57 apply (zenon_L631_); trivial. % 51.40/51.57 (* end of lemma zenon_L632_ *) % 51.40/51.57 assert (zenon_L633_ : (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.57 do 0 intro. intros zenon_Hd3 zenon_H62 zenon_H65 zenon_Hde zenon_Hfb zenon_H3b zenon_H318 zenon_H3d9 zenon_H2db zenon_H2ce zenon_H72 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_H2e0 zenon_H8c zenon_Hc2 zenon_H90 zenon_H35 zenon_Hcf zenon_H42 zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H131 zenon_H128 zenon_H12c zenon_H24 zenon_H324 zenon_H117 zenon_H105 zenon_Hff zenon_Ha2 zenon_H2e1 zenon_H23 zenon_H10b zenon_Hfe zenon_H2b zenon_Hf6 zenon_H327 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hcc zenon_H49 zenon_Hda zenon_Hb0 zenon_H3d zenon_H19. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.57 apply (zenon_L15_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.57 apply (zenon_L632_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.57 apply (zenon_L355_); trivial. % 51.40/51.57 apply (zenon_L37_); trivial. % 51.40/51.57 (* end of lemma zenon_L633_ *) % 51.40/51.57 assert (zenon_L634_ : ((op1 (e10) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.57 do 0 intro. intros zenon_He6 zenon_Hbe zenon_H126 zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H327 zenon_Hf6 zenon_H2b zenon_Hfe zenon_H10b zenon_H23 zenon_H2e1 zenon_Ha2 zenon_Hff zenon_H105 zenon_H117 zenon_H324 zenon_H24 zenon_H12c zenon_H128 zenon_H131 zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H8c zenon_H2e0 zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H72 zenon_H2ce zenon_H2db zenon_H3d9 zenon_H318 zenon_H3b zenon_Hfb zenon_Hde zenon_H65 zenon_H62 zenon_Hd3 zenon_H3d zenon_H19. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.57 apply (zenon_L304_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.57 apply (zenon_L42_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.57 apply (zenon_L633_); trivial. % 51.40/51.57 apply (zenon_L37_); trivial. % 51.40/51.57 (* end of lemma zenon_L634_ *) % 51.40/51.57 assert (zenon_L635_ : (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((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)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e13)) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H3d zenon_Hd3 zenon_H65 zenon_Hde zenon_Hfb zenon_H3b zenon_H318 zenon_H3d9 zenon_H2db zenon_H2ce zenon_H72 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H311 zenon_H123 zenon_H10e zenon_H95 zenon_H305 zenon_H2ff zenon_H2ba zenon_H1b zenon_H2d4 zenon_H30d zenon_H314 zenon_H2e0 zenon_Hc2 zenon_H90 zenon_H35 zenon_Hcf zenon_H42 zenon_H7d zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_Hf8 zenon_H4b zenon_H113 zenon_H31b zenon_H131 zenon_H128 zenon_H12c zenon_H24 zenon_H324 zenon_H117 zenon_H105 zenon_Hff zenon_Ha2 zenon_H2e1 zenon_H23 zenon_H10b zenon_Hfe zenon_H2b zenon_Hf6 zenon_H327 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_Hb0 zenon_H126 zenon_Hbe zenon_He6 zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.57 apply (zenon_L47_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.57 apply (zenon_L630_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.57 apply (zenon_L634_); trivial. % 51.40/51.57 apply (zenon_L24_); trivial. % 51.40/51.57 (* end of lemma zenon_L635_ *) % 51.40/51.57 assert (zenon_L636_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.40/51.57 do 0 intro. intros zenon_He1 zenon_Hea zenon_H49 zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H8c zenon_Hff zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_Hf8 zenon_Hb0 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H72 zenon_H2ce zenon_H7d zenon_H54 zenon_H90 zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H305 zenon_H2db zenon_H318 zenon_H23 zenon_Hfb zenon_H327 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_Hbe zenon_Hcb zenon_H3d zenon_H19 zenon_Hde zenon_H50 zenon_H42. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.57 apply (zenon_L630_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.57 apply (zenon_L299_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.57 apply (zenon_L287_); trivial. % 51.40/51.57 apply (zenon_L17_); trivial. % 51.40/51.57 (* end of lemma zenon_L636_ *) % 51.40/51.57 assert (zenon_L637_ : ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H126 zenon_H2db zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_Hff zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_Hf8 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_H311 zenon_H123 zenon_H10e zenon_H305 zenon_H318 zenon_H23 zenon_Hfb zenon_H327 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H95 zenon_Haf zenon_H4b zenon_Hb5 zenon_Hcb zenon_H90 zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H3d zenon_He1 zenon_H54 zenon_He2 zenon_H7d zenon_H49 zenon_Hda zenon_Hbe zenon_H42 zenon_H2ce zenon_He6 zenon_H65 zenon_H72 zenon_Hcf zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.57 apply (zenon_L47_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.57 apply (zenon_L636_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.57 apply (zenon_L374_); trivial. % 51.40/51.57 apply (zenon_L24_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.57 apply (zenon_L299_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.57 apply (zenon_L294_); trivial. % 51.40/51.57 apply (zenon_L319_); trivial. % 51.40/51.57 (* end of lemma zenon_L637_ *) % 51.40/51.57 assert (zenon_L638_ : (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_Hea zenon_Hff zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_Hf8 zenon_Hb0 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H305 zenon_H2db zenon_H318 zenon_H23 zenon_Hfb zenon_H327 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H95 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_Hcb zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H72 zenon_H65 zenon_He6 zenon_H2ce zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.57 apply (zenon_L370_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.57 apply (zenon_L283_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.57 apply (zenon_L39_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.57 apply (zenon_L637_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.57 apply (zenon_L41_); trivial. % 51.40/51.57 apply (zenon_L24_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.57 apply (zenon_L630_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.57 apply (zenon_L299_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.57 apply (zenon_L549_); trivial. % 51.40/51.57 apply (zenon_L320_); trivial. % 51.40/51.57 (* end of lemma zenon_L638_ *) % 51.40/51.57 assert (zenon_L639_ : (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H2b zenon_Hfe zenon_H10b zenon_H2e1 zenon_H117 zenon_H324 zenon_H24 zenon_H12c zenon_H128 zenon_H131 zenon_H31b zenon_H113 zenon_Hf6 zenon_He1 zenon_Hea zenon_Hff zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_Hf8 zenon_Hb0 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H7d zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H305 zenon_H2db zenon_H318 zenon_H23 zenon_Hfb zenon_H327 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H90 zenon_H35 zenon_H42 zenon_H72 zenon_H65 zenon_H54 zenon_H49 zenon_He6 zenon_H2ce zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.57 apply (zenon_L317_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.57 apply (zenon_L12_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.57 apply (zenon_L283_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.57 apply (zenon_L39_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.57 apply (zenon_L635_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.57 apply (zenon_L41_); trivial. % 51.40/51.57 apply (zenon_L24_); trivial. % 51.40/51.57 apply (zenon_L630_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.57 apply (zenon_L638_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.57 apply (zenon_L322_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.57 apply (zenon_L283_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.57 apply (zenon_L324_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.57 apply (zenon_L630_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.57 apply (zenon_L299_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.57 apply (zenon_L288_); trivial. % 51.40/51.57 apply (zenon_L321_); trivial. % 51.40/51.57 (* end of lemma zenon_L639_ *) % 51.40/51.57 assert (zenon_L640_ : ((op1 (e11) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H34 zenon_H46 zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_H327 zenon_Hfb zenon_H23 zenon_H318 zenon_H2db zenon_H305 zenon_H10e zenon_H123 zenon_H311 zenon_H2ff zenon_H30d zenon_H314 zenon_H2e0 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hf8 zenon_H3d9 zenon_Hff zenon_Hea zenon_Hf6 zenon_H113 zenon_H31b zenon_H131 zenon_H128 zenon_H12c zenon_H24 zenon_H324 zenon_H117 zenon_H2e1 zenon_H10b zenon_Hfe zenon_H2b zenon_Hd3 zenon_Hde zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H2c zenon_Hab zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H2be zenon_H2c9 zenon_H2c8 zenon_H125 zenon_H126 zenon_H2d1 zenon_H1c zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hcb zenon_H3d zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.57 apply (zenon_L86_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.57 apply (zenon_L13_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.57 apply (zenon_L298_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.57 apply (zenon_L639_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.57 apply (zenon_L298_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.57 apply (zenon_L626_); trivial. % 51.40/51.57 apply (zenon_L52_); trivial. % 51.40/51.57 (* end of lemma zenon_L640_ *) % 51.40/51.57 assert (zenon_L641_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.40/51.57 do 0 intro. intros zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_Hde zenon_He1 zenon_Hea zenon_H35 zenon_Hff zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_Hf8 zenon_Hb0 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H72 zenon_H2ce zenon_H7d zenon_H54 zenon_H90 zenon_H2e0 zenon_H314 zenon_H30d zenon_H2ff zenon_Haf zenon_H311 zenon_H123 zenon_H10e zenon_H305 zenon_H2db zenon_H318 zenon_H23 zenon_Hfb zenon_H327 zenon_H46 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hcf zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_Hb8 zenon_Hc8 zenon_H50 zenon_H42. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.57 apply (zenon_L630_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.57 apply (zenon_L13_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.57 apply (zenon_L549_); trivial. % 51.40/51.57 apply (zenon_L17_); trivial. % 51.40/51.57 (* end of lemma zenon_L641_ *) % 51.40/51.57 assert (zenon_L642_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_Hf8 zenon_H34 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H3d9 zenon_H2d1 zenon_H126 zenon_H125 zenon_H2c8 zenon_H2c9 zenon_H2be zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H95 zenon_H49 zenon_Haf zenon_H2ce zenon_H72 zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_Hc2 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H66 zenon_H65 zenon_Hde zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.57 apply (zenon_L86_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.57 apply (zenon_L299_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.57 apply (zenon_L311_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.57 apply (zenon_L321_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.57 apply (zenon_L311_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.57 apply (zenon_L626_); trivial. % 51.40/51.57 apply (zenon_L364_); trivial. % 51.40/51.57 (* end of lemma zenon_L642_ *) % 51.40/51.57 assert (zenon_L643_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H327 zenon_Ha3 zenon_Hcb zenon_Hf0 zenon_Hec zenon_H19 zenon_Hc2 zenon_Hf3 zenon_H35 zenon_Hbe zenon_H2c6 zenon_H7c zenon_H49 zenon_H2bf zenon_H33a zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.57 apply (zenon_L65_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.57 apply (zenon_L308_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.57 apply (zenon_L445_); trivial. % 51.40/51.57 apply (zenon_L46_); trivial. % 51.40/51.57 (* end of lemma zenon_L643_ *) % 51.40/51.57 assert (zenon_L644_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_Hcc zenon_H65 zenon_H66 zenon_H51 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.57 apply (zenon_L16_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.57 apply (zenon_L17_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.57 apply (zenon_L362_); trivial. % 51.40/51.57 apply (zenon_L24_); trivial. % 51.40/51.57 (* end of lemma zenon_L644_ *) % 51.40/51.57 assert (zenon_L645_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H3d9 zenon_H3d zenon_H2ce zenon_H46 zenon_H11a zenon_H335 zenon_Ha2 zenon_Hf6 zenon_H33 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H65 zenon_H66 zenon_H51 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.57 apply (zenon_L427_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.57 apply (zenon_L16_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.57 apply (zenon_L66_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.57 apply (zenon_L458_); trivial. % 51.40/51.57 apply (zenon_L24_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.57 apply (zenon_L626_); trivial. % 51.40/51.57 apply (zenon_L644_); trivial. % 51.40/51.57 (* end of lemma zenon_L645_ *) % 51.40/51.57 assert (zenon_L646_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.57 do 0 intro. intros zenon_Hb5 zenon_Hd3 zenon_H4b zenon_Hde zenon_H8c zenon_He1 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H33 zenon_Hf6 zenon_H335 zenon_H11a zenon_H46 zenon_H2ce zenon_H3d9 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.57 apply (zenon_L335_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.57 apply (zenon_L645_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.57 apply (zenon_L36_); trivial. % 51.40/51.57 apply (zenon_L37_); trivial. % 51.40/51.57 (* end of lemma zenon_L646_ *) % 51.40/51.57 assert (zenon_L647_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H33e zenon_Hcf zenon_H10e zenon_H10b zenon_H2b zenon_Hfe zenon_H62 zenon_H2c9 zenon_H30b zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H327 zenon_H3d zenon_Hb0 zenon_Ha3 zenon_Ha2 zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H3d9 zenon_H2ce zenon_H46 zenon_H11a zenon_Hf6 zenon_H33 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_He1 zenon_H8c zenon_Hde zenon_H4b zenon_Hd3 zenon_Hb5 zenon_H9e zenon_H19. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.40/51.57 apply (zenon_L80_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.40/51.57 apply (zenon_L457_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.40/51.57 apply (zenon_L646_); trivial. % 51.40/51.57 apply (zenon_L452_); trivial. % 51.40/51.57 (* end of lemma zenon_L647_ *) % 51.40/51.57 assert (zenon_L648_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e13)) = (e10)) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H9e zenon_Hb5 zenon_Hd3 zenon_H4b zenon_Hde zenon_H8c zenon_He1 zenon_Hda zenon_H35 zenon_H90 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H33 zenon_Hf6 zenon_H11a zenon_H46 zenon_H2ce zenon_H3d9 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H30b zenon_H2c9 zenon_H62 zenon_Hfe zenon_H2b zenon_H10b zenon_H10e zenon_Hcf zenon_H33e zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.57 apply (zenon_L647_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.57 apply (zenon_L40_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.57 apply (zenon_L43_); trivial. % 51.40/51.57 apply (zenon_L37_); trivial. % 51.40/51.57 (* end of lemma zenon_L648_ *) % 51.40/51.57 assert (zenon_L649_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.57 do 0 intro. intros zenon_H19 zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hbe zenon_H42 zenon_H33e zenon_Hcf zenon_H10e zenon_H10b zenon_H2b zenon_Hfe zenon_H62 zenon_H2c9 zenon_H30b zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_H54 zenon_Haf zenon_H3d9 zenon_H2ce zenon_H46 zenon_H11a zenon_Hf6 zenon_H33 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_He1 zenon_H8c zenon_Hde zenon_H4b zenon_Hb5 zenon_H9e zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.57 apply (zenon_L648_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.57 apply (zenon_L34_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.57 apply (zenon_L45_); trivial. % 51.40/51.57 apply (zenon_L46_); trivial. % 51.40/51.57 (* end of lemma zenon_L649_ *) % 51.40/51.57 assert (zenon_L650_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.57 do 0 intro. intros zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H9e zenon_Hb5 zenon_H4b zenon_Hde zenon_He1 zenon_H35 zenon_H90 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H33 zenon_Hf6 zenon_H11a zenon_H46 zenon_H2ce zenon_H3d9 zenon_Haf zenon_H54 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H30b zenon_H2c9 zenon_Hfe zenon_H2b zenon_H10b zenon_H10e zenon_Hcf zenon_H33e zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19 zenon_H8c. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.57 apply (zenon_L47_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.57 apply (zenon_L66_); trivial. % 51.40/51.57 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.57 apply (zenon_L649_); trivial. % 51.40/51.57 apply (zenon_L24_); trivial. % 51.40/51.57 (* end of lemma zenon_L650_ *) % 51.40/51.57 assert (zenon_L651_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H3d9 zenon_H11a zenon_H8c zenon_Hc2 zenon_Hcb zenon_Ha2 zenon_H65 zenon_H95 zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Hde zenon_H19 zenon_H3d zenon_He1 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L288_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.58 apply (zenon_L93_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.58 apply (zenon_L34_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.58 apply (zenon_L45_); trivial. % 51.40/51.58 apply (zenon_L46_); trivial. % 51.40/51.58 (* end of lemma zenon_L651_ *) % 51.40/51.58 assert (zenon_L652_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hf8 zenon_Hea zenon_He1 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H11a zenon_H3d9 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H50 zenon_H42. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.58 apply (zenon_L651_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.58 apply (zenon_L299_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.58 apply (zenon_L288_); trivial. % 51.40/51.58 apply (zenon_L17_); trivial. % 51.40/51.58 (* end of lemma zenon_L652_ *) % 51.40/51.58 assert (zenon_L653_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H3d9 zenon_H3d zenon_H19 zenon_Ha2 zenon_H335 zenon_H11a zenon_H46 zenon_H2ce zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Hde zenon_H65 zenon_H62 zenon_H66 zenon_H51 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L458_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L363_); trivial. % 51.40/51.58 (* end of lemma zenon_L653_ *) % 51.40/51.58 assert (zenon_L654_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H33e zenon_H10b zenon_H7c zenon_H327 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H8c zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H2c9 zenon_H30b zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H51 zenon_H66 zenon_H62 zenon_H65 zenon_Hde zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H2ce zenon_H46 zenon_H11a zenon_Ha2 zenon_H3d zenon_H3d9 zenon_H9e zenon_H19. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H33e); [ zenon_intro zenon_H10a | zenon_intro zenon_H33f ]. % 51.40/51.58 apply (zenon_L75_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H33f); [ zenon_intro zenon_H330 | zenon_intro zenon_H340 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.58 apply (zenon_L65_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.58 apply (zenon_L309_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.58 apply (zenon_L432_); trivial. % 51.40/51.58 apply (zenon_L46_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L363_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H340); [ zenon_intro zenon_H335 | zenon_intro zenon_H33b ]. % 51.40/51.58 apply (zenon_L653_); trivial. % 51.40/51.58 apply (zenon_L452_); trivial. % 51.40/51.58 (* end of lemma zenon_L654_ *) % 51.40/51.58 assert (zenon_L655_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H90 zenon_H42 zenon_Hcf zenon_H95 zenon_H4b zenon_Hb5 zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_Hea zenon_Hf8 zenon_H9e zenon_H3d9 zenon_H3d zenon_Ha2 zenon_H11a zenon_H46 zenon_H2ce zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Hde zenon_H65 zenon_H66 zenon_H51 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H30b zenon_H2c9 zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H327 zenon_H7c zenon_H10b zenon_H33e zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.58 apply (zenon_L47_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.58 apply (zenon_L652_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.58 apply (zenon_L654_); trivial. % 51.40/51.58 apply (zenon_L24_); trivial. % 51.40/51.58 (* end of lemma zenon_L655_ *) % 51.40/51.58 assert (zenon_L656_ : ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hbe zenon_H10e zenon_H2b zenon_Hfe zenon_Hb0 zenon_Haf zenon_Hf6 zenon_H33 zenon_H90 zenon_H42 zenon_Hcf zenon_H95 zenon_H4b zenon_Hb5 zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_Hea zenon_Hf8 zenon_H9e zenon_H3d9 zenon_H3d zenon_Ha2 zenon_H11a zenon_H46 zenon_H2ce zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Hde zenon_H65 zenon_H66 zenon_H54 zenon_He1 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H30b zenon_H2c9 zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H327 zenon_H7c zenon_H10b zenon_H33e zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.58 apply (zenon_L12_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.58 apply (zenon_L13_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.58 apply (zenon_L650_); trivial. % 51.40/51.58 apply (zenon_L655_); trivial. % 51.40/51.58 (* end of lemma zenon_L656_ *) % 51.40/51.58 assert (zenon_L657_ : (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H3dc zenon_H12c zenon_H126 zenon_Hbe zenon_Ha3 zenon_H19 zenon_Ha2 zenon_H65 zenon_H62 zenon_H66 zenon_H51 zenon_H54 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H1c zenon_H7c zenon_H49 zenon_H2c zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3dc); [ zenon_intro zenon_H321 | zenon_intro zenon_H3dd ]. % 51.40/51.58 apply (zenon_L387_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3dd); [ zenon_intro zenon_H335 | zenon_intro zenon_H3de ]. % 51.40/51.58 apply (zenon_L458_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3de); [ zenon_intro zenon_H304 | zenon_intro zenon_H3d3 ]. % 51.40/51.58 apply (zenon_L334_); trivial. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 (* end of lemma zenon_L657_ *) % 51.40/51.58 assert (zenon_L658_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hb5 zenon_Hda zenon_Hd3 zenon_H4b zenon_Hde zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H7c zenon_H305 zenon_H2ce zenon_H46 zenon_H11a zenon_H62 zenon_Hbe zenon_H126 zenon_H12c zenon_H3dc zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_Ha3 zenon_Hb0 zenon_H3d zenon_H19. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.58 apply (zenon_L335_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.58 apply (zenon_L657_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.58 apply (zenon_L36_); trivial. % 51.40/51.58 apply (zenon_L37_); trivial. % 51.40/51.58 (* end of lemma zenon_L658_ *) % 51.40/51.58 assert (zenon_L659_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H90 zenon_H35 zenon_Hcf zenon_H42 zenon_Hcb zenon_H3d zenon_Hb0 zenon_Ha3 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H3dc zenon_H12c zenon_H126 zenon_Hbe zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H7c zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_Hde zenon_H4b zenon_Hd3 zenon_Hda zenon_Hb5 zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.58 apply (zenon_L16_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.58 apply (zenon_L287_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.58 apply (zenon_L658_); trivial. % 51.40/51.58 apply (zenon_L24_); trivial. % 51.40/51.58 (* end of lemma zenon_L659_ *) % 51.40/51.58 assert (zenon_L660_ : (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H8c zenon_Hb5 zenon_Hda zenon_Hd3 zenon_H4b zenon_Hde zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H7c zenon_H305 zenon_H2ce zenon_H46 zenon_H11a zenon_H126 zenon_H12c zenon_H3dc zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H35 zenon_H90 zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.58 apply (zenon_L659_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.58 apply (zenon_L40_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.58 apply (zenon_L43_); trivial. % 51.40/51.58 apply (zenon_L37_); trivial. % 51.40/51.58 (* end of lemma zenon_L660_ *) % 51.40/51.58 assert (zenon_L661_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H3d9 zenon_H3d zenon_Hcb zenon_Hbe zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H3dc zenon_H12c zenon_H126 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H7c zenon_Hde zenon_H4b zenon_Hd3 zenon_Hb5 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L660_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L52_); trivial. % 51.40/51.58 (* end of lemma zenon_L661_ *) % 51.40/51.58 assert (zenon_L662_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hf8 zenon_H108 zenon_H45 zenon_H3d9 zenon_H3d zenon_Hcb zenon_Hbe zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H3dc zenon_H12c zenon_H126 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H7c zenon_Hde zenon_H4b zenon_Hd3 zenon_Hb5 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.58 apply (zenon_L328_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.58 apply (zenon_L13_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.58 apply (zenon_L660_); trivial. % 51.40/51.58 apply (zenon_L661_); trivial. % 51.40/51.58 (* end of lemma zenon_L662_ *) % 51.40/51.58 assert (zenon_L663_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H2e0 zenon_H10e zenon_H3d9 zenon_Hb0 zenon_Hab zenon_H2c zenon_Haf zenon_H3dc zenon_H12c zenon_H11a zenon_H2ce zenon_H305 zenon_H7c zenon_Hde zenon_Hd3 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_Hda zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_Hf8 zenon_H108 zenon_H46 zenon_H45 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hcf zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_Hb8 zenon_Hc8 zenon_H42. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.58 apply (zenon_L74_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.58 apply (zenon_L283_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.58 apply (zenon_L39_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.58 apply (zenon_L662_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.58 apply (zenon_L41_); trivial. % 51.40/51.58 apply (zenon_L24_); trivial. % 51.40/51.58 apply (zenon_L550_); trivial. % 51.40/51.58 (* end of lemma zenon_L663_ *) % 51.40/51.58 assert (zenon_L664_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hf8 zenon_H108 zenon_H46 zenon_H45 zenon_H19 zenon_H3d zenon_H49 zenon_H95 zenon_H66 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_H50 zenon_H42. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.58 apply (zenon_L328_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.58 apply (zenon_L13_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.58 apply (zenon_L285_); trivial. % 51.40/51.58 apply (zenon_L17_); trivial. % 51.40/51.58 (* end of lemma zenon_L664_ *) % 51.40/51.58 assert (zenon_L665_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H3d9 zenon_H3d zenon_H2c zenon_H7c zenon_H1c zenon_H305 zenon_H2ce zenon_H46 zenon_H11a zenon_Ha2 zenon_H19 zenon_Hbe zenon_H126 zenon_H12c zenon_H3dc zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_He1 zenon_H54 zenon_H51 zenon_H66 zenon_H62 zenon_H65 zenon_H49 zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L657_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L362_); trivial. % 51.40/51.58 (* end of lemma zenon_L665_ *) % 51.40/51.58 assert (zenon_L666_ : (((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)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e11) = (e13))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H90 zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H42 zenon_Hb5 zenon_H4b zenon_H9e zenon_H95 zenon_H45 zenon_H108 zenon_Hf8 zenon_Hda zenon_H49 zenon_H65 zenon_H66 zenon_H51 zenon_H54 zenon_He1 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3dc zenon_H12c zenon_H126 zenon_Hbe zenon_Ha2 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H1c zenon_H7c zenon_H2c zenon_H3d zenon_H3d9 zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.58 apply (zenon_L47_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.58 apply (zenon_L664_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.58 apply (zenon_L665_); trivial. % 51.40/51.58 apply (zenon_L24_); trivial. % 51.40/51.58 (* end of lemma zenon_L666_ *) % 51.40/51.58 assert (zenon_L667_ : (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (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)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e12)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e11) = (e13))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Haf zenon_Hb0 zenon_Hcb zenon_Hcf zenon_H90 zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H42 zenon_Hb5 zenon_H4b zenon_H9e zenon_H95 zenon_H45 zenon_H108 zenon_Hf8 zenon_Hda zenon_H49 zenon_H65 zenon_H66 zenon_H54 zenon_He1 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3dc zenon_H12c zenon_H126 zenon_Hbe zenon_Ha2 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H1c zenon_H7c zenon_H2c zenon_H3d zenon_H3d9 zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.58 apply (zenon_L328_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.58 apply (zenon_L13_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.58 apply (zenon_L659_); trivial. % 51.40/51.58 apply (zenon_L666_); trivial. % 51.40/51.58 (* end of lemma zenon_L667_ *) % 51.40/51.58 assert (zenon_L668_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hfe zenon_H2b zenon_H10b zenon_H49 zenon_H2e0 zenon_H10e zenon_Haf zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3dc zenon_H12c zenon_H2ce zenon_H305 zenon_H3d9 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hff zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H108 zenon_H23 zenon_Hfb zenon_H3d zenon_H11a zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.58 apply (zenon_L7_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.58 apply (zenon_L99_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.58 apply (zenon_L317_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.58 apply (zenon_L317_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.58 apply (zenon_L328_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.58 apply (zenon_L663_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.58 apply (zenon_L74_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.58 apply (zenon_L283_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.58 apply (zenon_L39_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.58 apply (zenon_L667_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.58 apply (zenon_L41_); trivial. % 51.40/51.58 apply (zenon_L24_); trivial. % 51.40/51.58 apply (zenon_L664_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_L15_); trivial. % 51.40/51.58 apply (zenon_L602_); trivial. % 51.40/51.58 (* end of lemma zenon_L668_ *) % 51.40/51.58 assert (zenon_L669_ : (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H4b zenon_Hde zenon_H11a zenon_H3d zenon_Hfb zenon_H23 zenon_H108 zenon_H8c zenon_H19 zenon_Hc2 zenon_H90 zenon_H35 zenon_Hcf zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_Hb8 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H45 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_Hff zenon_Ha2 zenon_H65 zenon_H95 zenon_H3d9 zenon_H305 zenon_H2ce zenon_H12c zenon_H3dc zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Haf zenon_H10e zenon_H2e0 zenon_H10b zenon_H2b zenon_Hfe zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.58 apply (zenon_L668_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.58 apply (zenon_L34_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.58 apply (zenon_L45_); trivial. % 51.40/51.58 apply (zenon_L46_); trivial. % 51.40/51.58 (* end of lemma zenon_L669_ *) % 51.40/51.58 assert (zenon_L670_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3d zenon_Hcb zenon_Ha3 zenon_H42 zenon_H90 zenon_H35 zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H3dc zenon_H12c zenon_H126 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H7c zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_Hde zenon_H4b zenon_Hd3 zenon_Hda zenon_Hb5 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.58 apply (zenon_L39_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.58 apply (zenon_L660_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.58 apply (zenon_L41_); trivial. % 51.40/51.58 apply (zenon_L24_); trivial. % 51.40/51.58 (* end of lemma zenon_L670_ *) % 51.40/51.58 assert (zenon_L671_ : (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H8c zenon_H19 zenon_Hc2 zenon_Hb5 zenon_H4b zenon_Hde zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H7c zenon_H305 zenon_H2ce zenon_H46 zenon_H11a zenon_H126 zenon_H12c zenon_H3dc zenon_Haf zenon_H54 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H35 zenon_H90 zenon_H42 zenon_Ha3 zenon_Hcb zenon_H3d zenon_Hb8 zenon_Hc8 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.58 apply (zenon_L670_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.58 apply (zenon_L34_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.58 apply (zenon_L45_); trivial. % 51.40/51.58 apply (zenon_L46_); trivial. % 51.40/51.58 (* end of lemma zenon_L671_ *) % 51.40/51.58 assert (zenon_L672_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hde zenon_Hcc zenon_H96 zenon_H9e zenon_H54 zenon_H95 zenon_H19 zenon_Hcf zenon_H4b zenon_He8 zenon_H8c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_H41 zenon_He1 zenon_H3d zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.58 apply (zenon_L346_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.58 apply (zenon_L34_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.58 apply (zenon_L45_); trivial. % 51.40/51.58 apply (zenon_L46_); trivial. % 51.40/51.58 (* end of lemma zenon_L672_ *) % 51.40/51.58 assert (zenon_L673_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hb5 zenon_H7d zenon_H49 zenon_H35 zenon_H90 zenon_H30d zenon_H72 zenon_H65 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_H10e zenon_H123 zenon_H311 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H8c zenon_He8 zenon_H4b zenon_Hcf zenon_H95 zenon_H54 zenon_H9e zenon_Hcc zenon_Hde zenon_H3d zenon_H19. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.58 apply (zenon_L15_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H121 | zenon_intro zenon_H312 ]. % 51.40/51.58 apply (zenon_L89_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H10a | zenon_intro zenon_H313 ]. % 51.40/51.58 apply (zenon_L508_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H7c | zenon_intro zenon_He2 ]. % 51.40/51.58 apply (zenon_L341_); trivial. % 51.40/51.58 apply (zenon_L52_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.58 apply (zenon_L672_); trivial. % 51.40/51.58 apply (zenon_L37_); trivial. % 51.40/51.58 (* end of lemma zenon_L673_ *) % 51.40/51.58 assert (zenon_L674_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H3d9 zenon_H11a zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H8c zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_H304 zenon_H305 zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_He8 zenon_H4b zenon_Hcf zenon_H95 zenon_H10e zenon_Hb5 zenon_Hd3 zenon_Hde zenon_H123 zenon_H311 zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_Hb0 zenon_H3d zenon_H19. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L65_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L356_); trivial. % 51.40/51.58 (* end of lemma zenon_L674_ *) % 51.40/51.58 assert (zenon_L675_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H314 zenon_H2c9 zenon_H65 zenon_H72 zenon_H30d zenon_H19 zenon_H3d zenon_Hb0 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_Haf zenon_H311 zenon_H123 zenon_Hde zenon_Hb5 zenon_H10e zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H305 zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H8c zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H11a zenon_H3d9 zenon_H2c zenon_H1c zenon_Hd3. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H314); [ zenon_intro zenon_H7c | zenon_intro zenon_H315 ]. % 51.40/51.58 apply (zenon_L341_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H316 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L65_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L673_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H304 | zenon_intro zenon_Hd2 ]. % 51.40/51.58 apply (zenon_L674_); trivial. % 51.40/51.58 apply (zenon_L45_); trivial. % 51.40/51.58 (* end of lemma zenon_L675_ *) % 51.40/51.58 assert (zenon_L676_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H3d9 zenon_Hb5 zenon_Hd3 zenon_H4b zenon_Hde zenon_H7c zenon_H305 zenon_H2ce zenon_H46 zenon_H11a zenon_Hbe zenon_H126 zenon_H12c zenon_H3dc zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_H3d zenon_Hcb zenon_Hcf zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H65 zenon_H66 zenon_H51 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L659_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L644_); trivial. % 51.40/51.58 (* end of lemma zenon_L676_ *) % 51.40/51.58 assert (zenon_L677_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_He1 zenon_H54 zenon_H51 zenon_H66 zenon_H65 zenon_H49 zenon_Hda zenon_H42 zenon_H35 zenon_H90 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_Hcf zenon_Hcb zenon_H3d zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H95 zenon_Hab zenon_H2c zenon_Haf zenon_H3dc zenon_H12c zenon_H126 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H7c zenon_Hde zenon_H4b zenon_Hd3 zenon_Hb5 zenon_H3d9 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.58 apply (zenon_L39_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.58 apply (zenon_L676_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.58 apply (zenon_L41_); trivial. % 51.40/51.58 apply (zenon_L24_); trivial. % 51.40/51.58 (* end of lemma zenon_L677_ *) % 51.40/51.58 assert (zenon_L678_ : (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H8c zenon_Hc2 zenon_H3d9 zenon_Hb5 zenon_Hd3 zenon_H4b zenon_Hde zenon_H7c zenon_H305 zenon_H2ce zenon_H46 zenon_H11a zenon_H126 zenon_H12c zenon_H3dc zenon_H95 zenon_Ha2 zenon_Hcb zenon_Hcf zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_H65 zenon_Hb8 zenon_Hc8 zenon_H314 zenon_H2c9 zenon_H72 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H7d zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H113 zenon_H31b zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hcc zenon_H49 zenon_Hda zenon_Hb0 zenon_H3d zenon_H19. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.58 apply (zenon_L335_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H31b); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H31c ]. % 51.40/51.58 apply (zenon_L39_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H31c); [ zenon_intro zenon_H114 | zenon_intro zenon_H31d ]. % 51.40/51.58 apply (zenon_L82_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_He8 | zenon_intro zenon_H66 ]. % 51.40/51.58 apply (zenon_L675_); trivial. % 51.40/51.58 apply (zenon_L677_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.58 apply (zenon_L355_); trivial. % 51.40/51.58 apply (zenon_L37_); trivial. % 51.40/51.58 (* end of lemma zenon_L678_ *) % 51.40/51.58 assert (zenon_L679_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H19 zenon_H3d zenon_Hb0 zenon_Hcc zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Haf zenon_H31b zenon_H113 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H7d zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H72 zenon_H2c9 zenon_H314 zenon_Hc8 zenon_Hb8 zenon_H65 zenon_H42 zenon_H35 zenon_H90 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_Hcf zenon_Hcb zenon_Ha2 zenon_H95 zenon_H3dc zenon_H12c zenon_H126 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H7c zenon_Hde zenon_H4b zenon_Hb5 zenon_H3d9 zenon_Hc2 zenon_H8c zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.58 apply (zenon_L678_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.58 apply (zenon_L34_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.58 apply (zenon_L45_); trivial. % 51.40/51.58 apply (zenon_L46_); trivial. % 51.40/51.58 (* end of lemma zenon_L679_ *) % 51.40/51.58 assert (zenon_L680_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.58 do 0 intro. intros zenon_H19 zenon_H3d zenon_Hb0 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Haf zenon_H31b zenon_H113 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H7d zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H72 zenon_H2c9 zenon_H314 zenon_Hc8 zenon_Hb8 zenon_H65 zenon_H42 zenon_H35 zenon_H90 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_Hcf zenon_Hcb zenon_Ha2 zenon_H95 zenon_H3dc zenon_H12c zenon_H126 zenon_H11a zenon_H46 zenon_H2ce zenon_H305 zenon_H7c zenon_Hde zenon_H4b zenon_Hb5 zenon_H3d9 zenon_Hc2 zenon_H8c zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.58 apply (zenon_L427_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.58 apply (zenon_L671_); trivial. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.58 apply (zenon_L626_); trivial. % 51.40/51.58 apply (zenon_L679_); trivial. % 51.40/51.58 (* end of lemma zenon_L680_ *) % 51.40/51.58 assert (zenon_L681_ : (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> False). % 51.40/51.58 do 0 intro. intros zenon_Hf6 zenon_H54 zenon_H125 zenon_H314 zenon_H72 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H7d zenon_H113 zenon_H31b zenon_Hb0 zenon_Haf zenon_H3dc zenon_H12c zenon_H305 zenon_H90 zenon_H46 zenon_H2ce zenon_H66 zenon_H2c9 zenon_H35 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H7c zenon_H10b zenon_H33e zenon_Hfb zenon_H23 zenon_Hff zenon_H2e0 zenon_H2b zenon_Hfe zenon_H318 zenon_Hf8 zenon_Hea zenon_He1 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H11a zenon_H3d9 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hde zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H42. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.58 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.59 apply (zenon_L74_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.59 apply (zenon_L39_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.59 apply (zenon_L656_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.59 apply (zenon_L41_); trivial. % 51.40/51.59 apply (zenon_L24_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.59 apply (zenon_L482_); trivial. % 51.40/51.59 apply (zenon_L33_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.59 apply (zenon_L283_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.59 apply (zenon_L669_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.59 apply (zenon_L680_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.59 apply (zenon_L13_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.59 apply (zenon_L671_); trivial. % 51.40/51.59 apply (zenon_L655_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.59 apply (zenon_L482_); trivial. % 51.40/51.59 apply (zenon_L33_); trivial. % 51.40/51.59 apply (zenon_L652_); trivial. % 51.40/51.59 (* end of lemma zenon_L681_ *) % 51.40/51.59 assert (zenon_L682_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((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)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H2d1 zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hde zenon_Hc2 zenon_H8c zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_H3d9 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_He1 zenon_Hea zenon_Hf8 zenon_H318 zenon_Hfe zenon_H2b zenon_H2e0 zenon_Hff zenon_H23 zenon_Hfb zenon_H33e zenon_H10b zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H35 zenon_H2c9 zenon_H66 zenon_H46 zenon_H90 zenon_H305 zenon_H12c zenon_H3dc zenon_H31b zenon_H113 zenon_H7d zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H314 zenon_H125 zenon_Hf6 zenon_H2c6 zenon_H7c zenon_Hf1 zenon_H33a zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H2ce zenon_H62 zenon_H72 zenon_H4b zenon_Hb5 zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H22 | zenon_intro zenon_H2d2 ]. % 51.40/51.59 apply (zenon_L38_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H2d2); [ zenon_intro zenon_H11a | zenon_intro zenon_H2d3 ]. % 51.40/51.59 apply (zenon_L681_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H2d3); [ zenon_intro zenon_H2bf | zenon_intro zenon_He6 ]. % 51.40/51.59 apply (zenon_L445_); trivial. % 51.40/51.59 apply (zenon_L293_); trivial. % 51.40/51.59 (* end of lemma zenon_L682_ *) % 51.40/51.59 assert (zenon_L683_ : (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e12)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H2db zenon_H2ff zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hbe zenon_H42 zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H33a zenon_Hf1 zenon_H7c zenon_H2c6 zenon_Hf6 zenon_H125 zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H7d zenon_H113 zenon_H31b zenon_H3dc zenon_H12c zenon_H305 zenon_H90 zenon_H46 zenon_H66 zenon_H2c9 zenon_H35 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H10b zenon_H33e zenon_Hfb zenon_H23 zenon_Hff zenon_H2e0 zenon_H2b zenon_Hfe zenon_H318 zenon_Hf8 zenon_Hea zenon_He1 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hc2 zenon_Hde zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H2d1 zenon_H19 zenon_H8c. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.59 apply (zenon_L16_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.59 apply (zenon_L636_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.59 apply (zenon_L682_); trivial. % 51.40/51.59 apply (zenon_L24_); trivial. % 51.40/51.59 (* end of lemma zenon_L683_ *) % 51.40/51.59 assert (zenon_L684_ : (~((e10) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((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)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H8c zenon_H2d1 zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hde zenon_Hc2 zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_H3d9 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_He1 zenon_Hea zenon_Hf8 zenon_H318 zenon_Hfe zenon_H2b zenon_H2e0 zenon_Hff zenon_H23 zenon_Hfb zenon_H33e zenon_H10b zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H35 zenon_H2c9 zenon_H46 zenon_H90 zenon_H305 zenon_H12c zenon_H3dc zenon_H31b zenon_H113 zenon_H7d zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H314 zenon_H125 zenon_Hf6 zenon_H2c6 zenon_H7c zenon_Hf1 zenon_H33a zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H2ce zenon_H72 zenon_H4b zenon_Hb5 zenon_H2ff zenon_H2db zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.59 apply (zenon_L683_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.59 apply (zenon_L40_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.59 apply (zenon_L43_); trivial. % 51.40/51.59 apply (zenon_L37_); trivial. % 51.40/51.59 (* end of lemma zenon_L684_ *) % 51.40/51.59 assert (zenon_L685_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((e10) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((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)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H31e zenon_H8c zenon_H2d1 zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hde zenon_Hc2 zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_H3d9 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_He1 zenon_Hea zenon_Hf8 zenon_H318 zenon_Hfe zenon_H2b zenon_H2e0 zenon_Hff zenon_H23 zenon_Hfb zenon_H33e zenon_H10b zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H35 zenon_H2c9 zenon_H46 zenon_H90 zenon_H305 zenon_H12c zenon_H3dc zenon_H31b zenon_H113 zenon_H7d zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H314 zenon_H125 zenon_Hf6 zenon_H2c6 zenon_H7c zenon_H33a zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H2ce zenon_H72 zenon_H4b zenon_Hb5 zenon_H2ff zenon_H2db zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.40/51.59 apply (zenon_L643_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.40/51.59 apply (zenon_L466_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.40/51.59 apply (zenon_L334_); trivial. % 51.40/51.59 apply (zenon_L684_); trivial. % 51.40/51.59 (* end of lemma zenon_L685_ *) % 51.40/51.59 assert (zenon_L686_ : (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (~((e10) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (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) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H3d zenon_Hcb zenon_Ha3 zenon_H42 zenon_H2db zenon_H2ff zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H2c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H33a zenon_H7c zenon_H2c6 zenon_Hf6 zenon_H125 zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H7d zenon_H113 zenon_H31b zenon_H3dc zenon_H12c zenon_H305 zenon_H90 zenon_H46 zenon_H2c9 zenon_H35 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H10b zenon_H33e zenon_Hfb zenon_H23 zenon_Hff zenon_H2e0 zenon_H2b zenon_Hfe zenon_H318 zenon_Hf8 zenon_Hea zenon_He1 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hde zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H2d1 zenon_H31e zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.59 apply (zenon_L39_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.59 apply (zenon_L685_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.59 apply (zenon_L41_); trivial. % 51.40/51.59 apply (zenon_L24_); trivial. % 51.40/51.59 (* end of lemma zenon_L686_ *) % 51.40/51.59 assert (zenon_L687_ : (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((e11) = (e12))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((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 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H3d zenon_Hb0 zenon_Hda zenon_H49 zenon_Hcc zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H327 zenon_Hf6 zenon_H2b zenon_Hfe zenon_H10b zenon_H23 zenon_H2e1 zenon_Ha2 zenon_Hff zenon_H105 zenon_H117 zenon_H324 zenon_H24 zenon_H12c zenon_H128 zenon_H131 zenon_H31b zenon_H113 zenon_H4b zenon_Hf8 zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H2e0 zenon_H314 zenon_H30d zenon_H2d4 zenon_H1b zenon_H2ba zenon_H2ff zenon_H305 zenon_H95 zenon_H10e zenon_H123 zenon_H311 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H72 zenon_H2ce zenon_H2db zenon_H3d9 zenon_H318 zenon_H3b zenon_Hfb zenon_Hde zenon_H65 zenon_Hd3 zenon_H19 zenon_H8c. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.59 apply (zenon_L16_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.59 apply (zenon_L93_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.59 apply (zenon_L633_); trivial. % 51.40/51.59 apply (zenon_L24_); trivial. % 51.40/51.59 (* end of lemma zenon_L687_ *) % 51.40/51.59 assert (zenon_L688_ : ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((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)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H1c zenon_Hc2 zenon_H31e zenon_H2d1 zenon_Hc8 zenon_Hb8 zenon_Hd3 zenon_Hde zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_H3d9 zenon_Hea zenon_Hf8 zenon_H318 zenon_Hfe zenon_H2b zenon_H2e0 zenon_Hff zenon_H23 zenon_Hfb zenon_H33e zenon_H10b zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H2c9 zenon_H46 zenon_H305 zenon_H12c zenon_H3dc zenon_H31b zenon_H113 zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H314 zenon_H125 zenon_Hf6 zenon_H2c6 zenon_H7c zenon_H33a zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hab zenon_H2c zenon_Haf zenon_H2ce zenon_H72 zenon_H4b zenon_Hb5 zenon_H2ff zenon_H2db zenon_Hcb zenon_H3d zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H49 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H19 zenon_H8c. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.59 apply (zenon_L638_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.59 apply (zenon_L686_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.59 apply (zenon_L626_); trivial. % 51.40/51.59 apply (zenon_L373_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.59 apply (zenon_L13_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.59 apply (zenon_L686_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.59 apply (zenon_L320_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.59 apply (zenon_L686_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.59 apply (zenon_L626_); trivial. % 51.40/51.59 apply (zenon_L52_); trivial. % 51.40/51.59 (* end of lemma zenon_L688_ *) % 51.40/51.59 assert (zenon_L689_ : (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H31e zenon_H2db zenon_H2ff zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hbe zenon_H42 zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_H49 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H33a zenon_H7c zenon_H2c6 zenon_Hf6 zenon_H125 zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H7d zenon_H113 zenon_H31b zenon_H3dc zenon_H12c zenon_H305 zenon_H90 zenon_H46 zenon_H66 zenon_H2c9 zenon_H35 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H10b zenon_H33e zenon_Hfb zenon_H23 zenon_Hff zenon_H2e0 zenon_H2b zenon_Hfe zenon_H318 zenon_Hf8 zenon_Hea zenon_He1 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3d9 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hc2 zenon_Hde zenon_Hd3 zenon_Hda zenon_Hb8 zenon_Hc8 zenon_H2d1 zenon_H19 zenon_H8c. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H31e); [ zenon_intro zenon_H2bf | zenon_intro zenon_H31f ]. % 51.40/51.59 apply (zenon_L643_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H12b | zenon_intro zenon_H320 ]. % 51.40/51.59 apply (zenon_L466_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_H320); [ zenon_intro zenon_H304 | zenon_intro zenon_Hf1 ]. % 51.40/51.59 apply (zenon_L334_); trivial. % 51.40/51.59 apply (zenon_L683_); trivial. % 51.40/51.59 (* end of lemma zenon_L689_ *) % 51.40/51.59 assert (zenon_L690_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (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) (e10)) = (op1 (e10) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((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)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((e11) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.59 do 0 intro. intros zenon_H2d1 zenon_Hc8 zenon_Hb8 zenon_Hda zenon_Hd3 zenon_Hde zenon_H2d4 zenon_H1b zenon_H105 zenon_H3b zenon_H2ba zenon_H45 zenon_H3d9 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_He1 zenon_Hea zenon_Hf8 zenon_H318 zenon_Hfe zenon_H2b zenon_H2e0 zenon_Hff zenon_H23 zenon_Hfb zenon_H33e zenon_H10b zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H35 zenon_H2c9 zenon_H66 zenon_H46 zenon_H90 zenon_H305 zenon_H12c zenon_H3dc zenon_H31b zenon_H113 zenon_H7d zenon_H10e zenon_H123 zenon_H311 zenon_H30d zenon_H314 zenon_H125 zenon_Hf6 zenon_H2c6 zenon_H7c zenon_H33a zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H2ce zenon_H72 zenon_H4b zenon_Hb5 zenon_H42 zenon_Ha3 zenon_Hcb zenon_H3d zenon_H2ff zenon_H2db zenon_H31e zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.59 apply (zenon_L39_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.59 apply (zenon_L689_); trivial. % 51.40/51.59 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.59 apply (zenon_L41_); trivial. % 51.40/51.59 apply (zenon_L24_); trivial. % 51.40/51.59 (* end of lemma zenon_L690_ *) % 51.40/51.59 assert (zenon_L691_ : (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.60 do 0 intro. intros zenon_Hc2 zenon_H31e zenon_H2db zenon_H2ff zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H49 zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H33a zenon_H7c zenon_H2c6 zenon_Hf6 zenon_H125 zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H7d zenon_H113 zenon_H31b zenon_H3dc zenon_H12c zenon_H305 zenon_H46 zenon_H2c9 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H10b zenon_H33e zenon_Hfb zenon_H23 zenon_Hff zenon_H2e0 zenon_H2b zenon_Hfe zenon_H318 zenon_Hf8 zenon_Hea zenon_H3d9 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hb8 zenon_Hc8 zenon_H2d1 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H51 zenon_H66 zenon_H65 zenon_Hde zenon_H19 zenon_H8c. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L321_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L690_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L364_); trivial. % 51.40/51.60 (* end of lemma zenon_L691_ *) % 51.40/51.60 assert (zenon_L692_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e13)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.60 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_Hd3 zenon_H66 zenon_H62 zenon_H65 zenon_Hde zenon_Haf zenon_H2c zenon_H1c zenon_Hab zenon_H54 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_Hcc zenon_H49 zenon_Hda zenon_Hb0 zenon_H3d zenon_H19. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.60 apply (zenon_L15_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.60 apply (zenon_L363_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.60 apply (zenon_L355_); trivial. % 51.40/51.60 apply (zenon_L37_); trivial. % 51.40/51.60 (* end of lemma zenon_L692_ *) % 51.40/51.60 assert (zenon_L693_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e13) (e12)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H90 zenon_H35 zenon_H42 zenon_H3d zenon_Hb0 zenon_Hda zenon_H49 zenon_Hcc zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_Hde zenon_H65 zenon_H66 zenon_Hd3 zenon_H4b zenon_Hb5 zenon_H19 zenon_H8c. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.60 apply (zenon_L47_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.60 apply (zenon_L93_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.60 apply (zenon_L692_); trivial. % 51.40/51.60 apply (zenon_L24_); trivial. % 51.40/51.60 (* end of lemma zenon_L693_ *) % 51.40/51.60 assert (zenon_L694_ : ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e12))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (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 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H126 zenon_Hc2 zenon_H31e zenon_H2db zenon_H2ff zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_H72 zenon_H2ce zenon_Haf zenon_H49 zenon_H95 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_H33a zenon_H7c zenon_H2c6 zenon_Hf6 zenon_H125 zenon_H314 zenon_H30d zenon_H311 zenon_H123 zenon_H10e zenon_H7d zenon_H113 zenon_H31b zenon_H3dc zenon_H12c zenon_H305 zenon_H46 zenon_H2c9 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_H10b zenon_H33e zenon_Hfb zenon_H23 zenon_Hff zenon_H2e0 zenon_H2b zenon_Hfe zenon_H318 zenon_Hf8 zenon_Hea zenon_H3d9 zenon_H45 zenon_H2ba zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hb8 zenon_Hc8 zenon_H2d1 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_H90 zenon_H35 zenon_H42 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_He1 zenon_H54 zenon_H66 zenon_H65 zenon_Hde zenon_H19 zenon_H8c. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L324_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L690_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L693_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.60 apply (zenon_L13_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.60 apply (zenon_L690_); trivial. % 51.40/51.60 apply (zenon_L691_); trivial. % 51.40/51.60 (* end of lemma zenon_L694_ *) % 51.40/51.60 assert (zenon_L695_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.60 do 0 intro. intros zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H2c8 zenon_H11a zenon_H2c9 zenon_H62 zenon_H72 zenon_H4b zenon_Hb5 zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.60 apply (zenon_L290_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.60 apply (zenon_L40_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.60 apply (zenon_L43_); trivial. % 51.40/51.60 apply (zenon_L37_); trivial. % 51.40/51.60 (* end of lemma zenon_L695_ *) % 51.40/51.60 assert (zenon_L696_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.60 do 0 intro. intros zenon_Hde zenon_H19 zenon_H3d zenon_Hcb zenon_Ha3 zenon_Hbe zenon_H42 zenon_Hb5 zenon_H4b zenon_H72 zenon_H62 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_Haf zenon_H54 zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.60 apply (zenon_L695_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.60 apply (zenon_L34_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.60 apply (zenon_L45_); trivial. % 51.40/51.60 apply (zenon_L46_); trivial. % 51.40/51.60 (* end of lemma zenon_L696_ *) % 51.40/51.60 assert (zenon_L697_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H90 zenon_H35 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H54 zenon_Haf zenon_H2c8 zenon_H11a zenon_H2c9 zenon_H72 zenon_H4b zenon_Hb5 zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_Hde zenon_H19 zenon_H8c. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.60 apply (zenon_L47_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.60 apply (zenon_L288_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.60 apply (zenon_L696_); trivial. % 51.40/51.60 apply (zenon_L24_); trivial. % 51.40/51.60 (* end of lemma zenon_L697_ *) % 51.40/51.60 assert (zenon_L698_ : (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H3d9 zenon_H3d zenon_Hcb zenon_Hbe zenon_Hb5 zenon_H4b zenon_H72 zenon_H2c9 zenon_H11a zenon_H2c8 zenon_Haf zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hb0 zenon_Hcf zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Hde zenon_H8c zenon_H19 zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L697_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L372_); trivial. % 51.40/51.60 (* end of lemma zenon_L698_ *) % 51.40/51.60 assert (zenon_L699_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_He1 zenon_H19 zenon_H8c zenon_Hde zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hcf zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Haf zenon_H11a zenon_H2c9 zenon_H72 zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_H3d9 zenon_H45 zenon_H46 zenon_H34 zenon_Hf8 zenon_Hbe zenon_H35. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.40/51.60 apply (zenon_L281_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.40/51.60 apply (zenon_L284_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.60 apply (zenon_L86_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.60 apply (zenon_L13_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.60 apply (zenon_L697_); trivial. % 51.40/51.60 apply (zenon_L698_); trivial. % 51.40/51.60 apply (zenon_L308_); trivial. % 51.40/51.60 (* end of lemma zenon_L699_ *) % 51.40/51.60 assert (zenon_L700_ : (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (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) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H3d zenon_Hcb zenon_Hbe zenon_H33e zenon_Hcf zenon_H10e zenon_H10b zenon_H2b zenon_Hfe zenon_H2c9 zenon_H30b zenon_Hc8 zenon_Hb8 zenon_Hc2 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H327 zenon_Hb0 zenon_Ha2 zenon_H65 zenon_H95 zenon_Haf zenon_H3d9 zenon_H2ce zenon_H46 zenon_H11a zenon_Hf6 zenon_H33 zenon_H4b zenon_Hb5 zenon_H9e zenon_H15e zenon_H349 zenon_H3cb zenon_H2ea zenon_H3d2 zenon_Hde zenon_H8c zenon_H19 zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L650_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L372_); trivial. % 51.40/51.60 (* end of lemma zenon_L700_ *) % 51.40/51.60 assert (zenon_L701_ : (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H318 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_He1 zenon_H8c zenon_Hde zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H9e zenon_Hb5 zenon_H4b zenon_H33 zenon_Hf6 zenon_H46 zenon_H2ce zenon_H3d9 zenon_Haf zenon_H95 zenon_H65 zenon_Ha2 zenon_Hb0 zenon_H327 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_H2c9 zenon_Hfe zenon_H2b zenon_H10b zenon_H10e zenon_Hcf zenon_H33e zenon_Hbe zenon_Hcb zenon_H3d zenon_H45 zenon_Hf8 zenon_H11a zenon_H125 zenon_H54 zenon_H19. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H108 | zenon_intro zenon_H319 ]. % 51.40/51.60 apply (zenon_L74_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H319); [ zenon_intro zenon_H30b | zenon_intro zenon_H31a ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.60 apply (zenon_L12_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.60 apply (zenon_L13_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.60 apply (zenon_L650_); trivial. % 51.40/51.60 apply (zenon_L700_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H129 | zenon_intro zenon_Ha5 ]. % 51.40/51.60 apply (zenon_L482_); trivial. % 51.40/51.60 apply (zenon_L33_); trivial. % 51.40/51.60 (* end of lemma zenon_L701_ *) % 51.40/51.60 assert (zenon_L702_ : (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> False). % 51.40/51.60 do 0 intro. intros zenon_Hf8 zenon_Hda zenon_Hd3 zenon_Hab zenon_Hc8 zenon_Hb8 zenon_H3d zenon_Hb5 zenon_H4b zenon_H9e zenon_Hea zenon_He1 zenon_Hcf zenon_H8c zenon_Hde zenon_H45 zenon_H2ba zenon_H2c zenon_H3b zenon_H105 zenon_H1b zenon_H2d4 zenon_Hcb zenon_Hf0 zenon_He8 zenon_Hec zenon_H19 zenon_H1c zenon_Hc2 zenon_Hf3 zenon_H50 zenon_H42. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.60 apply (zenon_L408_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.60 apply (zenon_L299_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.60 apply (zenon_L65_); trivial. % 51.40/51.60 apply (zenon_L17_); trivial. % 51.40/51.60 (* end of lemma zenon_L702_ *) % 51.40/51.60 assert (zenon_L703_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((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))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H13b zenon_H2d4 zenon_H314 zenon_H31b zenon_H30d zenon_H311 zenon_H318 zenon_H33e zenon_H327 zenon_H2e0 zenon_H3d2 zenon_H2ea zenon_H3cb zenon_H349 zenon_H15e zenon_H3dc zenon_H2ce zenon_H305 zenon_H3d9 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H2db zenon_H324 zenon_H2ff zenon_H32a zenon_H2be zenon_H341 zenon_H31e zenon_H33a zenon_H2d1 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H32a); [ zenon_intro zenon_H2d | zenon_intro zenon_H32b ]. % 51.40/51.60 apply (zenon_L7_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H32b); [ zenon_intro zenon_H2bb | zenon_intro zenon_H32c ]. % 51.40/51.60 apply (zenon_L281_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H32c); [ zenon_intro zenon_H2bf | zenon_intro zenon_H49 ]. % 51.40/51.60 apply (zenon_L282_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.60 apply (zenon_L7_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.60 apply (zenon_L317_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.60 apply (zenon_L317_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.60 apply (zenon_L86_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.60 apply (zenon_L9_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.60 apply (zenon_L283_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.40/51.60 apply (zenon_L281_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.40/51.60 apply (zenon_L284_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.40/51.60 apply (zenon_L640_); trivial. % 51.40/51.60 apply (zenon_L309_); trivial. % 51.40/51.60 apply (zenon_L641_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.60 apply (zenon_L9_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.60 apply (zenon_L283_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.40/51.60 apply (zenon_L281_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.40/51.60 apply (zenon_L284_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.40/51.60 apply (zenon_L642_); trivial. % 51.40/51.60 apply (zenon_L309_); trivial. % 51.40/51.60 apply (zenon_L314_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.60 apply (zenon_L639_); trivial. % 51.40/51.60 apply (zenon_L335_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.60 apply (zenon_L11_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.60 apply (zenon_L11_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.60 apply (zenon_L12_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.60 apply (zenon_L283_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.40/51.60 apply (zenon_L86_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L639_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L686_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L687_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.40/51.60 apply (zenon_L454_); trivial. % 51.40/51.60 apply (zenon_L34_); trivial. % 51.40/51.60 apply (zenon_L630_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.40/51.60 apply (zenon_L281_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.40/51.60 apply (zenon_L688_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.40/51.60 apply (zenon_L332_); trivial. % 51.40/51.60 apply (zenon_L309_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.40/51.60 apply (zenon_L9_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.60 apply (zenon_L12_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.60 apply (zenon_L299_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.60 apply (zenon_L690_); trivial. % 51.40/51.60 apply (zenon_L691_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.40/51.60 apply (zenon_L333_); trivial. % 51.40/51.60 apply (zenon_L34_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.60 apply (zenon_L283_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2bb | zenon_intro zenon_H2e4 ]. % 51.40/51.60 apply (zenon_L281_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H2e5 ]. % 51.40/51.60 apply (zenon_L694_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H2de ]. % 51.40/51.60 apply (zenon_L332_); trivial. % 51.40/51.60 apply (zenon_L309_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.60 apply (zenon_L630_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.60 apply (zenon_L13_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.60 apply (zenon_L285_); trivial. % 51.40/51.60 apply (zenon_L17_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.60 apply (zenon_L639_); trivial. % 51.40/51.60 apply (zenon_L335_); trivial. % 51.40/51.60 apply (zenon_L629_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.40/51.60 apply (zenon_L426_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.60 apply (zenon_L7_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.60 apply (zenon_L317_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.60 apply (zenon_L317_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.60 apply (zenon_L86_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.60 apply (zenon_L39_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.60 apply (zenon_L699_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.60 apply (zenon_L41_); trivial. % 51.40/51.60 apply (zenon_L24_); trivial. % 51.40/51.60 apply (zenon_L594_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_L335_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.60 apply (zenon_L11_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.60 apply (zenon_L11_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.60 apply (zenon_L12_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.60 apply (zenon_L283_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.60 apply (zenon_L680_); trivial. % 51.40/51.60 apply (zenon_L651_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.60 apply (zenon_L39_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.60 apply (zenon_L701_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.60 apply (zenon_L41_); trivial. % 51.40/51.60 apply (zenon_L24_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.60 apply (zenon_L283_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.60 apply (zenon_L680_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.60 apply (zenon_L299_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.60 apply (zenon_L671_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L671_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L372_); trivial. % 51.40/51.60 apply (zenon_L652_); trivial. % 51.40/51.60 apply (zenon_L681_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_L335_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.60 apply (zenon_L317_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.60 apply (zenon_L317_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.60 apply (zenon_L12_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.60 apply (zenon_L283_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H314); [ zenon_intro zenon_H7c | zenon_intro zenon_H315 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L65_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L679_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H315); [ zenon_intro zenon_H2c8 | zenon_intro zenon_H316 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L65_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.60 apply (zenon_L673_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.60 apply (zenon_L34_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.60 apply (zenon_L45_); trivial. % 51.40/51.60 apply (zenon_L46_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H316); [ zenon_intro zenon_H304 | zenon_intro zenon_Hd2 ]. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3d9); [ zenon_intro zenon_He6 | zenon_intro zenon_H3da ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3da); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H3db ]. % 51.40/51.60 apply (zenon_L65_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_H3d3 | zenon_intro zenon_Hcc ]. % 51.40/51.60 apply (zenon_L626_); trivial. % 51.40/51.60 apply (zenon_L379_); trivial. % 51.40/51.60 apply (zenon_L45_); trivial. % 51.40/51.60 apply (zenon_L702_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.60 apply (zenon_L352_); trivial. % 51.40/51.60 apply (zenon_L57_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.60 apply (zenon_L427_); trivial. % 51.40/51.60 apply (zenon_L335_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.40/51.60 apply (zenon_L669_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.40/51.60 apply (zenon_L512_); trivial. % 51.40/51.60 apply (zenon_L82_); trivial. % 51.40/51.60 apply (zenon_L85_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.40/51.60 apply (zenon_L4_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.40/51.60 apply (zenon_L109_); trivial. % 51.40/51.60 apply (zenon_L47_); trivial. % 51.40/51.60 (* end of lemma zenon_L703_ *) % 51.40/51.60 assert (zenon_L704_ : (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((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) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((op2 (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 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H3df zenon_H1ac zenon_H176 zenon_H3c8 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d1 zenon_H33a zenon_H31e zenon_H341 zenon_H2be zenon_H32a zenon_H2ff zenon_H324 zenon_H2db zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3d9 zenon_H305 zenon_H2ce zenon_H3dc zenon_H349 zenon_H2ea zenon_H3d2 zenon_H2e0 zenon_H327 zenon_H33e zenon_H318 zenon_H311 zenon_H30d zenon_H31b zenon_H314 zenon_H2d4 zenon_H13b zenon_H245 zenon_H244 zenon_H14e zenon_H1ec zenon_H1bd zenon_H1e6 zenon_H19b zenon_H1cc zenon_H1cd zenon_H1f3 zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3df); [ zenon_intro zenon_H252 | zenon_intro zenon_H3e0 ]. % 51.40/51.60 apply (zenon_L536_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3e0); [ zenon_intro zenon_H3c9 | zenon_intro zenon_H3e1 ]. % 51.40/51.60 apply (zenon_L624_); trivial. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H3e1); [ zenon_intro zenon_H3cb | zenon_intro zenon_H1e7 ]. % 51.40/51.60 apply (zenon_L703_); trivial. % 51.40/51.60 apply (zenon_L518_); trivial. % 51.40/51.60 (* end of lemma zenon_L704_ *) % 51.40/51.60 assert (zenon_L705_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e21))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e21) (e22)) = (e23)) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.60 do 0 intro. intros zenon_H222 zenon_H1f3 zenon_H1ec zenon_H187 zenon_H15e zenon_H175 zenon_H1e6 zenon_H1bd zenon_H1c9 zenon_H1cc zenon_H1d7 zenon_H1d8 zenon_H176 zenon_H156 zenon_H1b1 zenon_H1ac zenon_H1fa zenon_H210 zenon_H14 zenon_H209 zenon_H205 zenon_H1fd zenon_H214 zenon_H284 zenon_H283 zenon_H1f7 zenon_H14e. % 51.40/51.60 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.40/51.61 apply (zenon_L150_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.40/51.61 apply (zenon_L155_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.40/51.61 apply (zenon_L216_); trivial. % 51.40/51.61 apply (zenon_L149_); trivial. % 51.40/51.61 (* end of lemma zenon_L705_ *) % 51.40/51.61 assert (zenon_L706_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e22)) = (e23)) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H22f zenon_H16f zenon_H16d zenon_H1a7 zenon_H1f7 zenon_H283 zenon_H284 zenon_H214 zenon_H1fd zenon_H205 zenon_H209 zenon_H14 zenon_H1fa zenon_H1ac zenon_H1b1 zenon_H156 zenon_H176 zenon_H1d8 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H175 zenon_H15e zenon_H187 zenon_H1ec zenon_H1f3 zenon_H222 zenon_H14e zenon_H210. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.61 apply (zenon_L129_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.61 apply (zenon_L130_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.61 apply (zenon_L705_); trivial. % 51.40/51.61 apply (zenon_L154_); trivial. % 51.40/51.61 (* end of lemma zenon_L706_ *) % 51.40/51.61 assert (zenon_L707_ : (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((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))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e20)) = (e22)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H22e zenon_H21b zenon_H217 zenon_H21f zenon_H13b zenon_H2d4 zenon_H314 zenon_H31b zenon_H30d zenon_H311 zenon_H318 zenon_H33e zenon_H327 zenon_H2e0 zenon_H3d2 zenon_H2ea zenon_H349 zenon_H3dc zenon_H2ce zenon_H305 zenon_H3d9 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H2db zenon_H324 zenon_H2ff zenon_H32a zenon_H2be zenon_H341 zenon_H31e zenon_H33a zenon_H2d1 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H22f zenon_H16d zenon_H1a7 zenon_H1f7 zenon_H283 zenon_H205 zenon_H1fa zenon_H1ac zenon_H1b1 zenon_H156 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H175 zenon_H1ec zenon_H1f3 zenon_H222 zenon_H24e zenon_H2b7 zenon_H3e2 zenon_H19f zenon_H168 zenon_H230 zenon_H210 zenon_H14e zenon_H209 zenon_H16f zenon_H1fd zenon_H214 zenon_H225 zenon_H176 zenon_H19b zenon_H180 zenon_H18e zenon_H195 zenon_H164 zenon_H22b zenon_H15e zenon_H14 zenon_H187. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H16e | zenon_intro zenon_H231 ]. % 51.40/51.61 apply (zenon_L120_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17c | zenon_intro zenon_H232 ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H169 | zenon_intro zenon_H233 ]. % 51.40/51.61 apply (zenon_L118_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H17f | zenon_intro zenon_H234 ]. % 51.40/51.61 apply (zenon_L127_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H19e | zenon_intro zenon_H1d8 ]. % 51.40/51.61 apply (zenon_L128_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H256 | zenon_intro zenon_H3e3 ]. % 51.40/51.61 apply (zenon_L277_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_H284 | zenon_intro zenon_H3e4 ]. % 51.40/51.61 apply (zenon_L706_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e4); [ zenon_intro zenon_H3cb | zenon_intro zenon_H21d ]. % 51.40/51.61 apply (zenon_L703_); trivial. % 51.40/51.61 apply (zenon_L159_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17f | zenon_intro zenon_H186 ]. % 51.40/51.61 apply (zenon_L164_); trivial. % 51.40/51.61 apply (zenon_L124_); trivial. % 51.40/51.61 (* end of lemma zenon_L707_ *) % 51.40/51.61 assert (zenon_L708_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> ((op2 (e23) (e20)) = (e22)) -> (~((e20) = (e21))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e21) (e22)) = (e23)) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H222 zenon_H1ac zenon_H21c zenon_H210 zenon_H14 zenon_H209 zenon_H205 zenon_H1fd zenon_H214 zenon_H284 zenon_H283 zenon_H1f7 zenon_H14e. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.40/51.61 apply (zenon_L192_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.40/51.61 apply (zenon_L155_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.40/51.61 apply (zenon_L216_); trivial. % 51.40/51.61 apply (zenon_L149_); trivial. % 51.40/51.61 (* end of lemma zenon_L708_ *) % 51.40/51.61 assert (zenon_L709_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H22f zenon_H16f zenon_H1f7 zenon_H254 zenon_H205 zenon_H19b zenon_H1ac zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H1fa zenon_H195 zenon_H175 zenon_H21d zenon_H1b1 zenon_H252 zenon_H17f zenon_H267 zenon_H1d7 zenon_H14e zenon_H210. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.61 apply (zenon_L129_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.61 apply (zenon_L515_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.61 apply (zenon_L206_); trivial. % 51.40/51.61 apply (zenon_L154_); trivial. % 51.40/51.61 (* end of lemma zenon_L709_ *) % 51.40/51.61 assert (zenon_L710_ : (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((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) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H3e2 zenon_H156 zenon_H283 zenon_H214 zenon_H1fd zenon_H209 zenon_H21c zenon_H222 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d1 zenon_H33a zenon_H31e zenon_H341 zenon_H2be zenon_H32a zenon_H2ff zenon_H324 zenon_H2db zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3d9 zenon_H305 zenon_H2ce zenon_H3dc zenon_H349 zenon_H2ea zenon_H3d2 zenon_H2e0 zenon_H327 zenon_H33e zenon_H318 zenon_H311 zenon_H30d zenon_H31b zenon_H314 zenon_H2d4 zenon_H13b zenon_H22f zenon_H16f zenon_H1f7 zenon_H254 zenon_H205 zenon_H19b zenon_H1ac zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H1fa zenon_H195 zenon_H175 zenon_H1b1 zenon_H252 zenon_H17f zenon_H267 zenon_H1d7 zenon_H14e zenon_H210. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H256 | zenon_intro zenon_H3e3 ]. % 51.40/51.61 apply (zenon_L193_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_H284 | zenon_intro zenon_H3e4 ]. % 51.40/51.61 apply (zenon_L708_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e4); [ zenon_intro zenon_H3cb | zenon_intro zenon_H21d ]. % 51.40/51.61 apply (zenon_L703_); trivial. % 51.40/51.61 apply (zenon_L709_); trivial. % 51.40/51.61 (* end of lemma zenon_L710_ *) % 51.40/51.61 assert (zenon_L711_ : ((op2 (e21) (e22)) = (e22)) -> ((op2 (e21) (e22)) = (e23)) -> (~((e22) = (e23))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H17f zenon_H284 zenon_H1ac. % 51.40/51.61 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H1ad | zenon_intro zenon_H14c ]. % 51.40/51.61 cut (((e23) = (e23)) = ((e22) = (e23))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H1ac. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H1ad. % 51.40/51.61 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.40/51.61 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 51.40/51.61 congruence. % 51.40/51.61 cut (((op2 (e21) (e22)) = (e22)) = ((e23) = (e22))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H1ae. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H17f. % 51.40/51.61 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 51.40/51.61 cut (((op2 (e21) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H3e5]. % 51.40/51.61 congruence. % 51.40/51.61 exact (zenon_H3e5 zenon_H284). % 51.40/51.61 apply zenon_H171. apply refl_equal. % 51.40/51.61 apply zenon_H14c. apply refl_equal. % 51.40/51.61 apply zenon_H14c. apply refl_equal. % 51.40/51.61 (* end of lemma zenon_L711_ *) % 51.40/51.61 assert (zenon_L712_ : (((op2 (op2 (e23) (e20)) (op2 (e23) (e20))) = (e20))/\(((op2 (op2 (e23) (e21)) (op2 (e23) (e21))) = (e21))/\(((op2 (op2 (e23) (e22)) (op2 (e23) (e22))) = (e22))/\((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e23)) -> False). % 51.40/51.61 do 0 intro. intros zenon_H1d6 zenon_H36d zenon_H14e zenon_H3c9. % 51.40/51.61 apply (zenon_and_s _ _ zenon_H1d6). zenon_intro zenon_H1da. zenon_intro zenon_H1d9. % 51.40/51.61 apply (zenon_and_s _ _ zenon_H1d9). zenon_intro zenon_H1dc. zenon_intro zenon_H1db. % 51.40/51.61 apply (zenon_and_s _ _ zenon_H1db). zenon_intro zenon_H1de. zenon_intro zenon_H1dd. % 51.40/51.61 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e23)) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H36d. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H1dd. % 51.40/51.61 cut (((e23) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H3ca]. % 51.40/51.61 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 51.40/51.61 congruence. % 51.40/51.61 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H246 | zenon_intro zenon_H247 ]. % 51.40/51.61 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H24a. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H246. % 51.40/51.61 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 51.40/51.61 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 51.40/51.61 congruence. % 51.40/51.61 apply (zenon_L171_); trivial. % 51.40/51.61 apply zenon_H247. apply refl_equal. % 51.40/51.61 apply zenon_H247. apply refl_equal. % 51.40/51.61 apply zenon_H3ca. apply sym_equal. exact zenon_H3c9. % 51.40/51.61 (* end of lemma zenon_L712_ *) % 51.40/51.61 assert (zenon_L713_ : ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e23)) -> False). % 51.40/51.61 do 0 intro. intros zenon_H21d zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H203 zenon_H26e zenon_H26d zenon_H36d zenon_H14e zenon_H3c9. % 51.40/51.61 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.40/51.61 apply (zenon_L169_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.40/51.61 apply (zenon_L134_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.40/51.61 apply (zenon_L204_); trivial. % 51.40/51.61 apply (zenon_L712_); trivial. % 51.40/51.61 (* end of lemma zenon_L713_ *) % 51.40/51.61 assert (zenon_L714_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e21)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H3c9 zenon_H36d zenon_H26d zenon_H26e zenon_H1bc zenon_H1bd zenon_H1d7 zenon_H175 zenon_H21d zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.40/51.61 apply (zenon_L151_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.40/51.61 apply (zenon_L713_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.40/51.61 apply (zenon_L153_); trivial. % 51.40/51.61 apply (zenon_L154_); trivial. % 51.40/51.61 (* end of lemma zenon_L714_ *) % 51.40/51.61 assert (zenon_L715_ : ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e23)) -> False). % 51.40/51.61 do 0 intro. intros zenon_H21d zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H252 zenon_H1c9 zenon_H1b1 zenon_H36d zenon_H14e zenon_H3c9. % 51.40/51.61 apply (zenon_or_s _ _ ax11); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1e2 ]. % 51.40/51.61 apply (zenon_L169_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1e3 ]. % 51.40/51.61 apply (zenon_L134_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H1e3); [ zenon_intro zenon_H1cb | zenon_intro zenon_H1d6 ]. % 51.40/51.61 apply (zenon_L185_); trivial. % 51.40/51.61 apply (zenon_L712_); trivial. % 51.40/51.61 (* end of lemma zenon_L715_ *) % 51.40/51.61 assert (zenon_L716_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e23)) -> False). % 51.40/51.61 do 0 intro. intros zenon_H273 zenon_H254 zenon_H210 zenon_H209 zenon_H26d zenon_H1fd zenon_H214 zenon_H262 zenon_H14 zenon_H21c zenon_H15e zenon_H21d zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H1c9 zenon_H1b1 zenon_H36d zenon_H14e zenon_H3c9. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H266 | zenon_intro zenon_H274 ]. % 51.40/51.61 apply (zenon_L198_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H26e | zenon_intro zenon_H275 ]. % 51.40/51.61 apply (zenon_L714_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H176 | zenon_intro zenon_H252 ]. % 51.40/51.61 apply (zenon_L197_); trivial. % 51.40/51.61 apply (zenon_L715_); trivial. % 51.40/51.61 (* end of lemma zenon_L716_ *) % 51.40/51.61 assert (zenon_L717_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e23) (e20)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H22f zenon_H195 zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H205 zenon_H3c9 zenon_H36d zenon_H1b1 zenon_H1bc zenon_H1bd zenon_H1d7 zenon_H175 zenon_H21d zenon_H15e zenon_H21c zenon_H14 zenon_H262 zenon_H214 zenon_H1fd zenon_H26d zenon_H209 zenon_H254 zenon_H273 zenon_H14e zenon_H210. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.61 apply (zenon_L183_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.61 apply (zenon_L184_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.61 apply (zenon_L716_); trivial. % 51.40/51.61 apply (zenon_L154_); trivial. % 51.40/51.61 (* end of lemma zenon_L717_ *) % 51.40/51.61 assert (zenon_L718_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e21)) = (e23)) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H222 zenon_H1ac zenon_H210 zenon_H273 zenon_H254 zenon_H209 zenon_H26d zenon_H1fd zenon_H214 zenon_H262 zenon_H14 zenon_H21c zenon_H15e zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1bc zenon_H1b1 zenon_H36d zenon_H3c9 zenon_H205 zenon_H19b zenon_H16f zenon_H187 zenon_H18e zenon_H195 zenon_H22f zenon_H1f7 zenon_H14e. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.40/51.61 apply (zenon_L192_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.40/51.61 apply (zenon_L155_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.40/51.61 apply (zenon_L717_); trivial. % 51.40/51.61 apply (zenon_L149_); trivial. % 51.40/51.61 (* end of lemma zenon_L718_ *) % 51.40/51.61 assert (zenon_L719_ : (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> ((op2 (e22) (e21)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op2 (e23) (e20)) = (e22)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e20) = (e21))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H1fa zenon_H22f zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H205 zenon_H3c9 zenon_H36d zenon_H1b1 zenon_H1bd zenon_H15e zenon_H21c zenon_H14 zenon_H262 zenon_H214 zenon_H1fd zenon_H26d zenon_H209 zenon_H254 zenon_H273 zenon_H210 zenon_H1ac zenon_H222 zenon_H195 zenon_H175 zenon_H21d zenon_H1ec zenon_H17f zenon_H267 zenon_H1d7 zenon_H1f7 zenon_H14e. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.40/51.61 apply (zenon_L132_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.40/51.61 apply (zenon_L718_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.40/51.61 apply (zenon_L202_); trivial. % 51.40/51.61 apply (zenon_L149_); trivial. % 51.40/51.61 (* end of lemma zenon_L719_ *) % 51.40/51.61 assert (zenon_L720_ : (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e22) (e23)) = (e23)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e22)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H210 zenon_H14e zenon_H209 zenon_H22f zenon_H19b zenon_H1e7 zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H1d7 zenon_H214 zenon_H1fd zenon_H16f zenon_H1ac zenon_H24e zenon_H1ec zenon_H256 zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H1d8 zenon_H217 zenon_H21f zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H19b); [ zenon_intro zenon_H175 | zenon_intro zenon_H19c ]. % 51.40/51.61 apply (zenon_L271_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H19c); [ zenon_intro zenon_H186 | zenon_intro zenon_H19d ]. % 51.40/51.61 apply (zenon_L124_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H19d); [ zenon_intro zenon_H18d | zenon_intro zenon_H194 ]. % 51.40/51.61 apply (zenon_L125_); trivial. % 51.40/51.61 apply (zenon_L126_); trivial. % 51.40/51.61 (* end of lemma zenon_L720_ *) % 51.40/51.61 assert (zenon_L721_ : (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e23)) = (e23)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H2b6 zenon_H23c zenon_H24b zenon_H18e zenon_H187 zenon_H21f zenon_H217 zenon_H21b zenon_H1f3 zenon_H2b7 zenon_H256 zenon_H1ec zenon_H24e zenon_H1ac zenon_H16f zenon_H1fd zenon_H214 zenon_H1d7 zenon_H1cc zenon_H1bd zenon_H1e6 zenon_H1e7 zenon_H19b zenon_H22f zenon_H209 zenon_H14e zenon_H210 zenon_H15e zenon_H14 zenon_H195. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.40/51.61 apply (zenon_L263_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.40/51.61 apply (zenon_L163_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.40/51.61 apply (zenon_L720_); trivial. % 51.40/51.61 apply (zenon_L126_); trivial. % 51.40/51.61 (* end of lemma zenon_L721_ *) % 51.40/51.61 assert (zenon_L722_ : (((op2 (e22) (e20)) = (e23))\/(((op2 (e22) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e22) (e23)) = (e23))))) -> ((op2 (e20) (e22)) = (e20)) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((e20) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((e20) = (e21))) -> ((op2 (e23) (e20)) = (e22)) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((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) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H3df zenon_H156 zenon_H273 zenon_H254 zenon_H26d zenon_H262 zenon_H1b1 zenon_H36d zenon_H1fa zenon_H3e2 zenon_H22f zenon_H19b zenon_H1e6 zenon_H1bd zenon_H1cc zenon_H16f zenon_H24e zenon_H2b7 zenon_H1f3 zenon_H21b zenon_H217 zenon_H21f zenon_H187 zenon_H18e zenon_H24b zenon_H23c zenon_H2b6 zenon_H14e zenon_H1f7 zenon_H283 zenon_H214 zenon_H1fd zenon_H205 zenon_H209 zenon_H14 zenon_H210 zenon_H21c zenon_H1ac zenon_H222 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d1 zenon_H33a zenon_H31e zenon_H341 zenon_H2be zenon_H32a zenon_H2ff zenon_H324 zenon_H2db zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3d9 zenon_H305 zenon_H2ce zenon_H3dc zenon_H15e zenon_H349 zenon_H2ea zenon_H3d2 zenon_H2e0 zenon_H327 zenon_H33e zenon_H318 zenon_H311 zenon_H30d zenon_H31b zenon_H314 zenon_H2d4 zenon_H13b zenon_H1d7 zenon_H267 zenon_H17f zenon_H1ec zenon_H175 zenon_H195. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3df); [ zenon_intro zenon_H252 | zenon_intro zenon_H3e0 ]. % 51.40/51.61 apply (zenon_L710_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e0); [ zenon_intro zenon_H3c9 | zenon_intro zenon_H3e1 ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H256 | zenon_intro zenon_H3e3 ]. % 51.40/51.61 apply (zenon_L263_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_H284 | zenon_intro zenon_H3e4 ]. % 51.40/51.61 apply (zenon_L711_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e4); [ zenon_intro zenon_H3cb | zenon_intro zenon_H21d ]. % 51.40/51.61 apply (zenon_L703_); trivial. % 51.40/51.61 apply (zenon_L719_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e1); [ zenon_intro zenon_H3cb | zenon_intro zenon_H1e7 ]. % 51.40/51.61 apply (zenon_L703_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H256 | zenon_intro zenon_H3e3 ]. % 51.40/51.61 apply (zenon_L721_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_H284 | zenon_intro zenon_H3e4 ]. % 51.40/51.61 apply (zenon_L708_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e4); [ zenon_intro zenon_H3cb | zenon_intro zenon_H21d ]. % 51.40/51.61 apply (zenon_L703_); trivial. % 51.40/51.61 apply (zenon_L202_); trivial. % 51.40/51.61 (* end of lemma zenon_L722_ *) % 51.40/51.61 assert (zenon_L723_ : (((op2 (e20) (e22)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e10) (e12)) = (e11))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e12)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e12)) = (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/((op1 (e11) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((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) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e21) = (e23))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H3e2 zenon_H2b6 zenon_H21b zenon_H23c zenon_H24b zenon_H21c zenon_H222 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d1 zenon_H33a zenon_H31e zenon_H341 zenon_H2be zenon_H32a zenon_H2ff zenon_H324 zenon_H2db zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3d9 zenon_H305 zenon_H2ce zenon_H3dc zenon_H349 zenon_H2ea zenon_H3d2 zenon_H2e0 zenon_H327 zenon_H33e zenon_H318 zenon_H311 zenon_H30d zenon_H31b zenon_H314 zenon_H2d4 zenon_H13b zenon_H214 zenon_H1fd zenon_H1f7 zenon_H285 zenon_H273 zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H26d zenon_H19f zenon_H19e zenon_H15e zenon_H1bd zenon_H1b1 zenon_H19b zenon_H187 zenon_H18e zenon_H27c zenon_H1f3 zenon_H280 zenon_H27f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H283 zenon_H1ac zenon_H1fa zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e2); [ zenon_intro zenon_H256 | zenon_intro zenon_H3e3 ]. % 51.40/51.61 apply (zenon_L263_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_H284 | zenon_intro zenon_H3e4 ]. % 51.40/51.61 apply (zenon_L708_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H3e4); [ zenon_intro zenon_H3cb | zenon_intro zenon_H21d ]. % 51.40/51.61 apply (zenon_L703_); trivial. % 51.40/51.61 apply (zenon_L219_); trivial. % 51.40/51.61 (* end of lemma zenon_L723_ *) % 51.40/51.61 assert (zenon_L724_ : ((op2 (e22) (e23)) = (e20)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H1c9 zenon_H349 zenon_H15e zenon_H2ea zenon_H14 zenon_H3e6. % 51.40/51.61 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H3e8 ]. % 51.40/51.61 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H3e6. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H3e7. % 51.40/51.61 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3e8]. % 51.40/51.61 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H3e9]. % 51.40/51.61 congruence. % 51.40/51.61 cut (((op2 (e22) (e23)) = (e20)) = ((op2 (h4 (e12)) (h4 (e13))) = (op2 (e23) (op2 (e23) (e23))))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H3e9. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H1c9. % 51.40/51.61 cut (((e20) = (op2 (e23) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 51.40/51.61 cut (((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3ea]. % 51.40/51.61 congruence. % 51.40/51.61 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H3e8 ]. % 51.40/51.61 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H3ea. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H3e7. % 51.40/51.61 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3e8]. % 51.40/51.61 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3eb]. % 51.40/51.61 congruence. % 51.40/51.61 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H399]. % 51.40/51.61 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.40/51.61 congruence. % 51.40/51.61 apply (zenon_L487_); trivial. % 51.40/51.61 exact (zenon_H399 zenon_H2ea). % 51.40/51.61 apply zenon_H3e8. apply refl_equal. % 51.40/51.61 apply zenon_H3e8. apply refl_equal. % 51.40/51.61 exact (zenon_H148 zenon_H14). % 51.40/51.61 apply zenon_H3e8. apply refl_equal. % 51.40/51.61 apply zenon_H3e8. apply refl_equal. % 51.40/51.61 (* end of lemma zenon_L724_ *) % 51.40/51.61 assert (zenon_L725_ : (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.40/51.61 do 0 intro. intros zenon_H3ec zenon_H13 zenon_H62 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea. % 51.40/51.61 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H3ec. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H13. % 51.40/51.61 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3e6]. % 51.40/51.61 cut (((h4 (e10)) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3ed]. % 51.40/51.61 congruence. % 51.40/51.61 elim (classic ((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [ zenon_intro zenon_H3ee | zenon_intro zenon_H3ef ]. % 51.40/51.61 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13)))) = ((h4 (e10)) = (h4 (op1 (e12) (e13))))). % 51.40/51.61 intro zenon_D_pnotp. % 51.40/51.61 apply zenon_H3ed. % 51.40/51.61 rewrite <- zenon_D_pnotp. % 51.40/51.61 exact zenon_H3ee. % 51.40/51.61 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3ef]. % 51.40/51.61 cut (((h4 (op1 (e12) (e13))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3f0]. % 51.40/51.61 congruence. % 51.40/51.61 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3f1]. % 51.40/51.61 congruence. % 51.40/51.61 exact (zenon_H3f1 zenon_H62). % 51.40/51.61 apply zenon_H3ef. apply refl_equal. % 51.40/51.61 apply zenon_H3ef. apply refl_equal. % 51.40/51.61 apply (zenon_L724_); trivial. % 51.40/51.61 (* end of lemma zenon_L725_ *) % 51.40/51.61 assert (zenon_L726_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H90 zenon_H35 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hcf zenon_H95 zenon_H65 zenon_H9e zenon_Ha2 zenon_H4b zenon_Hb5 zenon_H42 zenon_Hbe zenon_Ha3 zenon_Hcb zenon_H3d zenon_Hde zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.61 apply (zenon_L47_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.61 apply (zenon_L287_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L725_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L726_ *) % 51.40/51.61 assert (zenon_L727_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_Hde zenon_H3d zenon_Hcb zenon_Ha3 zenon_H42 zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.61 apply (zenon_L39_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.61 apply (zenon_L726_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L727_ *) % 51.40/51.61 assert (zenon_L728_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e13)) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H90 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H42 zenon_H51 zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.61 apply (zenon_L47_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.61 apply (zenon_L17_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L725_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L728_ *) % 51.40/51.61 assert (zenon_L729_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H90 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H2db zenon_H126 zenon_Hbe zenon_H1c zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.61 apply (zenon_L47_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.61 apply (zenon_L303_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L725_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L729_ *) % 51.40/51.61 assert (zenon_L730_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H126 zenon_H2db zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.61 apply (zenon_L39_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.61 apply (zenon_L729_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L730_ *) % 51.40/51.61 assert (zenon_L731_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H2e0 zenon_H10e zenon_H90 zenon_H35 zenon_H2db zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_Hcf zenon_He8 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_H3d zenon_Hb8 zenon_Hc8 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.61 apply (zenon_L12_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.61 apply (zenon_L283_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.61 apply (zenon_L730_); trivial. % 51.40/51.61 apply (zenon_L408_); trivial. % 51.40/51.61 (* end of lemma zenon_L731_ *) % 51.40/51.61 assert (zenon_L732_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H42 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H90 zenon_Hf1 zenon_He1 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_H95 zenon_H49 zenon_H3d zenon_H19. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.61 apply (zenon_L15_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.61 apply (zenon_L728_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.61 apply (zenon_L337_); trivial. % 51.40/51.61 apply (zenon_L37_); trivial. % 51.40/51.61 (* end of lemma zenon_L732_ *) % 51.40/51.61 assert (zenon_L733_ : (((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 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H327 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_Hc2 zenon_H2db zenon_H10e zenon_H2e0 zenon_Hbe zenon_Hd3 zenon_Hab zenon_Hb5 zenon_H4b zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H42 zenon_Hde zenon_H35 zenon_H90 zenon_He1 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_H95 zenon_H3d zenon_H19 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.61 apply (zenon_L731_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.61 apply (zenon_L308_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.61 apply (zenon_L732_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.61 apply (zenon_L34_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.61 apply (zenon_L45_); trivial. % 51.40/51.61 apply (zenon_L46_); trivial. % 51.40/51.61 apply (zenon_L46_); trivial. % 51.40/51.61 (* end of lemma zenon_L733_ *) % 51.40/51.61 assert (zenon_L734_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hda zenon_H2c zenon_H3d zenon_H95 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_He1 zenon_H90 zenon_H35 zenon_Hde zenon_H42 zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H4b zenon_Hb5 zenon_Hab zenon_Hd3 zenon_H2e0 zenon_H10e zenon_H2db zenon_Hcf zenon_Hb8 zenon_Hc8 zenon_H327 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.61 apply (zenon_L39_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.61 apply (zenon_L733_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L734_ *) % 51.40/51.61 assert (zenon_L735_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H90 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H42 zenon_Hc8 zenon_Hb8 zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_Ha2 zenon_H9e zenon_H65 zenon_H95 zenon_H49 zenon_Hcf zenon_Hc2 zenon_H1c zenon_H45 zenon_H46 zenon_H108 zenon_Hf8 zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.61 apply (zenon_L47_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.61 apply (zenon_L550_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L725_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L735_ *) % 51.40/51.61 assert (zenon_L736_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((e10) = (e11))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H324 zenon_He6 zenon_H90 zenon_Hda zenon_Hd3 zenon_Hde zenon_H2db zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H3d zenon_H131 zenon_H12c zenon_Hbe zenon_H108 zenon_H128 zenon_H8c zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H7c zenon_H2ff zenon_H2ba zenon_H2e1 zenon_Hb0 zenon_Ha2 zenon_H9e zenon_H65 zenon_H66 zenon_H95 zenon_H49 zenon_H54 zenon_Hab zenon_H2c zenon_Haf zenon_H50 zenon_H42 zenon_H4b zenon_Hb5 zenon_H1c zenon_H19 zenon_Hc2. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.40/51.61 apply (zenon_L56_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.40/51.61 apply (zenon_L730_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.40/51.61 apply (zenon_L389_); trivial. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 (* end of lemma zenon_L736_ *) % 51.40/51.61 assert (zenon_L737_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H90 zenon_H35 zenon_H3d zenon_Hb5 zenon_H4b zenon_H42 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H41 zenon_He1 zenon_Hbe zenon_He8 zenon_Hcf zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.61 apply (zenon_L16_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.61 apply (zenon_L94_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L725_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L737_ *) % 51.40/51.61 assert (zenon_L738_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_Hcf zenon_He8 zenon_He1 zenon_H41 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_H42 zenon_H4b zenon_Hb5 zenon_H3d zenon_H35 zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.61 apply (zenon_L39_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.61 apply (zenon_L737_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 (* end of lemma zenon_L738_ *) % 51.40/51.61 assert (zenon_L739_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> ((op1 (e10) (e11)) = (e11)) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((e12) = (e13))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H2e0 zenon_H104 zenon_H2e1 zenon_H2ba zenon_H2ff zenon_H23 zenon_Hc2 zenon_H19 zenon_H1c zenon_H3d zenon_Hb5 zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H54 zenon_Hde zenon_Hcb zenon_Hf3 zenon_Hec zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_H131 zenon_Hc8 zenon_Hb8 zenon_Hcf zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H2db zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H10e zenon_H72 zenon_Haf zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H125 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hea zenon_H136 zenon_H324 zenon_H4b. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.61 apply (zenon_L7_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.61 apply (zenon_L99_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.61 apply (zenon_L317_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.61 apply (zenon_L735_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.61 apply (zenon_L317_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.61 apply (zenon_L328_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.61 apply (zenon_L74_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.61 apply (zenon_L283_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.61 apply (zenon_L730_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.40/51.61 apply (zenon_L56_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.40/51.61 apply (zenon_L730_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.40/51.61 apply (zenon_L391_); trivial. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.61 apply (zenon_L83_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.61 apply (zenon_L283_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.61 apply (zenon_L730_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.61 apply (zenon_L39_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.61 apply (zenon_L736_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 apply (zenon_L24_); trivial. % 51.40/51.61 apply (zenon_L335_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.61 apply (zenon_L317_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.61 apply (zenon_L738_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.40/51.61 apply (zenon_L109_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.40/51.61 apply (zenon_L730_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.40/51.61 apply (zenon_L419_); trivial. % 51.40/51.61 apply (zenon_L41_); trivial. % 51.40/51.61 apply (zenon_L57_); trivial. % 51.40/51.61 (* end of lemma zenon_L739_ *) % 51.40/51.61 assert (zenon_L740_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H42 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H90 zenon_Hf1 zenon_He1 zenon_H10e zenon_H10a zenon_Hbe zenon_H65 zenon_H50 zenon_H66 zenon_H95 zenon_H49 zenon_H3d zenon_H19. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.61 apply (zenon_L15_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.61 apply (zenon_L728_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.61 apply (zenon_L423_); trivial. % 51.40/51.61 apply (zenon_L37_); trivial. % 51.40/51.61 (* end of lemma zenon_L740_ *) % 51.40/51.61 assert (zenon_L741_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((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)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H327 zenon_Hc2 zenon_Hb8 zenon_Hc8 zenon_Hd3 zenon_Hab zenon_Hb5 zenon_H4b zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H42 zenon_Hde zenon_H35 zenon_H90 zenon_He1 zenon_H10e zenon_H10a zenon_Hbe zenon_H65 zenon_H50 zenon_H66 zenon_H95 zenon_H3d zenon_H19 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.61 apply (zenon_L57_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.61 apply (zenon_L309_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.61 apply (zenon_L740_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.61 apply (zenon_L34_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.61 apply (zenon_L45_); trivial. % 51.40/51.61 apply (zenon_L46_); trivial. % 51.40/51.61 apply (zenon_L46_); trivial. % 51.40/51.61 (* end of lemma zenon_L741_ *) % 51.40/51.61 assert (zenon_L742_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e12)) = (e13)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hde zenon_Ha3 zenon_H19 zenon_Ha2 zenon_H96 zenon_H9e zenon_H65 zenon_H50 zenon_H66 zenon_H95 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.61 apply (zenon_L32_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.61 apply (zenon_L34_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.61 apply (zenon_L45_); trivial. % 51.40/51.61 apply (zenon_L46_); trivial. % 51.40/51.61 (* end of lemma zenon_L742_ *) % 51.40/51.61 assert (zenon_L743_ : (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e13)) = (e13)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.61 do 0 intro. intros zenon_H131 zenon_H12c zenon_Hbe zenon_H321 zenon_H11a zenon_H125 zenon_H49 zenon_H7c zenon_H2c6 zenon_Hde zenon_H19 zenon_Ha2 zenon_H96 zenon_H9e zenon_H65 zenon_H50 zenon_H66 zenon_H95 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H131); [ zenon_intro zenon_H126 | zenon_intro zenon_H132 ]. % 51.40/51.61 apply (zenon_L387_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H132); [ zenon_intro zenon_H129 | zenon_intro zenon_H133 ]. % 51.40/51.61 apply (zenon_L482_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H12b | zenon_intro zenon_Ha3 ]. % 51.40/51.61 apply (zenon_L331_); trivial. % 51.40/51.61 apply (zenon_L742_); trivial. % 51.40/51.61 (* end of lemma zenon_L743_ *) % 51.40/51.61 assert (zenon_L744_ : (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hb5 zenon_H4b zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H42 zenon_H35 zenon_H90 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H95 zenon_H66 zenon_H50 zenon_H65 zenon_H9e zenon_Ha2 zenon_Hde zenon_H2c6 zenon_H7c zenon_H49 zenon_H125 zenon_H11a zenon_H321 zenon_Hbe zenon_H12c zenon_H131 zenon_H3d zenon_H19. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.61 apply (zenon_L15_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.61 apply (zenon_L728_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.61 apply (zenon_L743_); trivial. % 51.40/51.61 apply (zenon_L37_); trivial. % 51.40/51.61 (* end of lemma zenon_L744_ *) % 51.40/51.61 assert (zenon_L745_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e11) (e11)) = (e12)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((e10) = (e11))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.61 do 0 intro. intros zenon_Hcf zenon_H131 zenon_H12c zenon_H321 zenon_H11a zenon_H125 zenon_H7c zenon_H2c6 zenon_Hde zenon_Ha2 zenon_H65 zenon_H95 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_H90 zenon_H35 zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H8c zenon_Hbe zenon_He1 zenon_H41 zenon_H50 zenon_Hea zenon_H9e zenon_H49 zenon_Hda zenon_H42 zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.61 apply (zenon_L744_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.61 apply (zenon_L40_); trivial. % 51.40/51.61 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.61 apply (zenon_L93_); trivial. % 51.40/51.61 apply (zenon_L37_); trivial. % 51.40/51.61 (* end of lemma zenon_L745_ *) % 51.40/51.61 assert (zenon_L746_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e11)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H324 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hfb zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H128 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_H2db zenon_H3d zenon_Hb5 zenon_H4b zenon_H42 zenon_Hda zenon_H49 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_He1 zenon_Hbe zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H35 zenon_H90 zenon_H2c zenon_Hd3 zenon_Hab zenon_H95 zenon_H65 zenon_Ha2 zenon_Hde zenon_H2c6 zenon_H7c zenon_H125 zenon_H11a zenon_H12c zenon_H131 zenon_Hcf zenon_H1c zenon_H19 zenon_Hc2. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.40/51.62 apply (zenon_L109_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.40/51.62 apply (zenon_L303_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.40/51.62 apply (zenon_L745_); trivial. % 51.40/51.62 apply (zenon_L41_); trivial. % 51.40/51.62 (* end of lemma zenon_L746_ *) % 51.40/51.62 assert (zenon_L747_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e10)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H341 zenon_H2c9 zenon_H2c5 zenon_H42 zenon_H50 zenon_Hde zenon_H19 zenon_H3d zenon_Hcb zenon_Hb5 zenon_H4b zenon_H9e zenon_H65 zenon_H95 zenon_Hcf zenon_Hd3 zenon_Hda zenon_H45 zenon_H46 zenon_H324 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hfb zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H128 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_H2db zenon_Hea zenon_He1 zenon_H8c zenon_H3ec zenon_H13 zenon_H1c9 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H90 zenon_H125 zenon_H11a zenon_H12c zenon_H131 zenon_Hc2 zenon_H35 zenon_Hbe zenon_H49 zenon_H7c zenon_H2ff zenon_Ha2 zenon_H2ba zenon_H2e1 zenon_H2c zenon_H1c zenon_Hab. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H341); [ zenon_intro zenon_H34 | zenon_intro zenon_H342 ]. % 51.40/51.62 apply (zenon_L591_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H342); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H343 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.62 apply (zenon_L746_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.62 apply (zenon_L13_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.62 apply (zenon_L287_); trivial. % 51.40/51.62 apply (zenon_L17_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H343); [ zenon_intro zenon_H12b | zenon_intro zenon_Haa ]. % 51.40/51.62 apply (zenon_L371_); trivial. % 51.40/51.62 apply (zenon_L34_); trivial. % 51.40/51.62 (* end of lemma zenon_L747_ *) % 51.40/51.62 assert (zenon_L748_ : (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((e10) = (e11))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e10) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H2e1 zenon_H2ba zenon_Ha2 zenon_H2ff zenon_H7c zenon_Hbe zenon_H35 zenon_Hc2 zenon_H131 zenon_H12c zenon_H11a zenon_H125 zenon_H90 zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H8c zenon_He1 zenon_Hea zenon_H2db zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_Hf0 zenon_Hec zenon_Hf3 zenon_H128 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_Hfb zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H324 zenon_H46 zenon_H45 zenon_Hcf zenon_H95 zenon_H65 zenon_H9e zenon_H4b zenon_Hb5 zenon_Hcb zenon_H3d zenon_H19 zenon_Hde zenon_H50 zenon_H42 zenon_H2c5 zenon_H2c9 zenon_H341 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.62 apply (zenon_L747_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.62 apply (zenon_L34_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.62 apply (zenon_L45_); trivial. % 51.40/51.62 apply (zenon_L46_); trivial. % 51.40/51.62 (* end of lemma zenon_L748_ *) % 51.40/51.62 assert (zenon_L749_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> ((op1 (e11) (e13)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.62 do 0 intro. intros zenon_Hde zenon_H42 zenon_H50 zenon_Hf3 zenon_Hc2 zenon_H19 zenon_Hec zenon_He8 zenon_Hf0 zenon_Hcb zenon_H45 zenon_H46 zenon_Hc8 zenon_Hb8 zenon_H3d zenon_Hb5 zenon_H4b zenon_H9e zenon_Hea zenon_He1 zenon_Hcf zenon_H8c zenon_Hf8 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.62 apply (zenon_L627_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.62 apply (zenon_L34_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.62 apply (zenon_L45_); trivial. % 51.40/51.62 apply (zenon_L46_); trivial. % 51.40/51.62 (* end of lemma zenon_L749_ *) % 51.40/51.62 assert (zenon_L750_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H13b zenon_H2db zenon_H2e0 zenon_H2ff zenon_H324 zenon_H341 zenon_H2d4 zenon_H2ea zenon_H15e zenon_H349 zenon_H14 zenon_H1c9 zenon_H13 zenon_H3ec zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H327 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.62 apply (zenon_L12_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.62 apply (zenon_L299_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.62 apply (zenon_L727_); trivial. % 51.40/51.62 apply (zenon_L728_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.62 apply (zenon_L283_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.62 apply (zenon_L730_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.62 apply (zenon_L734_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.62 apply (zenon_L299_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.62 apply (zenon_L727_); trivial. % 51.40/51.62 apply (zenon_L728_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.40/51.62 apply (zenon_L73_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.62 apply (zenon_L739_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.62 apply (zenon_L34_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.62 apply (zenon_L45_); trivial. % 51.40/51.62 apply (zenon_L46_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.62 apply (zenon_L7_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.62 apply (zenon_L317_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.62 apply (zenon_L86_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.62 apply (zenon_L421_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.62 apply (zenon_L81_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.62 apply (zenon_L283_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.62 apply (zenon_L730_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.62 apply (zenon_L39_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.62 apply (zenon_L741_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.62 apply (zenon_L41_); trivial. % 51.40/51.62 apply (zenon_L24_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.62 apply (zenon_L75_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.62 apply (zenon_L317_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.62 apply (zenon_L731_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.62 apply (zenon_L421_); trivial. % 51.40/51.62 apply (zenon_L57_); trivial. % 51.40/51.62 apply (zenon_L82_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.62 apply (zenon_L7_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.62 apply (zenon_L86_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.62 apply (zenon_L299_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.62 apply (zenon_L727_); trivial. % 51.40/51.62 apply (zenon_L728_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.62 apply (zenon_L11_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.62 apply (zenon_L12_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.62 apply (zenon_L13_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.62 apply (zenon_L727_); trivial. % 51.40/51.62 apply (zenon_L728_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.62 apply (zenon_L283_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.62 apply (zenon_L730_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.62 apply (zenon_L39_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.62 apply (zenon_L748_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.62 apply (zenon_L41_); trivial. % 51.40/51.62 apply (zenon_L24_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.62 apply (zenon_L427_); trivial. % 51.40/51.62 apply (zenon_L335_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.62 apply (zenon_L317_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.62 apply (zenon_L317_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.62 apply (zenon_L12_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.62 apply (zenon_L283_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.62 apply (zenon_L730_); trivial. % 51.40/51.62 apply (zenon_L749_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.62 apply (zenon_L352_); trivial. % 51.40/51.62 apply (zenon_L57_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.62 apply (zenon_L427_); trivial. % 51.40/51.62 apply (zenon_L335_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.62 apply (zenon_L317_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.62 apply (zenon_L328_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.62 apply (zenon_L13_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.62 apply (zenon_L727_); trivial. % 51.40/51.62 apply (zenon_L728_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.62 apply (zenon_L427_); trivial. % 51.40/51.62 apply (zenon_L335_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.40/51.62 apply (zenon_L512_); trivial. % 51.40/51.62 apply (zenon_L82_); trivial. % 51.40/51.62 apply (zenon_L85_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.40/51.62 apply (zenon_L4_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.40/51.62 apply (zenon_L109_); trivial. % 51.40/51.62 apply (zenon_L47_); trivial. % 51.40/51.62 (* end of lemma zenon_L750_ *) % 51.40/51.62 assert (zenon_L751_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e23)) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H22f zenon_H16f zenon_H175 zenon_H1f7 zenon_H254 zenon_H252 zenon_H205 zenon_H19b zenon_H1ac zenon_H187 zenon_H18e zenon_H195 zenon_H1fa zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H327 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3ec zenon_H13 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H2d4 zenon_H341 zenon_H324 zenon_H2ff zenon_H2e0 zenon_H2db zenon_H13b zenon_H14e zenon_H210. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.62 apply (zenon_L129_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.62 apply (zenon_L515_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.62 apply (zenon_L750_); trivial. % 51.40/51.62 apply (zenon_L154_); trivial. % 51.40/51.62 (* end of lemma zenon_L751_ *) % 51.40/51.62 assert (zenon_L752_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e21) = (e23))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H22f zenon_H195 zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H1f7 zenon_H175 zenon_H1e6 zenon_H1cd zenon_H1cc zenon_H1ec zenon_H244 zenon_H245 zenon_H205 zenon_H1ac zenon_H1fa zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H327 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3ec zenon_H13 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H2d4 zenon_H341 zenon_H324 zenon_H2ff zenon_H2e0 zenon_H2db zenon_H13b zenon_H14e zenon_H210. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.62 apply (zenon_L183_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.62 apply (zenon_L243_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.62 apply (zenon_L750_); trivial. % 51.40/51.62 apply (zenon_L154_); trivial. % 51.40/51.62 (* end of lemma zenon_L752_ *) % 51.40/51.62 assert (zenon_L753_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H22f zenon_H16f zenon_H175 zenon_H16d zenon_H1a7 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H327 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3ec zenon_H13 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H2d4 zenon_H341 zenon_H324 zenon_H2ff zenon_H2e0 zenon_H2db zenon_H13b zenon_H14e zenon_H210. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.62 apply (zenon_L129_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.62 apply (zenon_L130_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.62 apply (zenon_L750_); trivial. % 51.40/51.62 apply (zenon_L154_); trivial. % 51.40/51.62 (* end of lemma zenon_L753_ *) % 51.40/51.62 assert (zenon_L754_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H28d zenon_H15d zenon_H164 zenon_H168 zenon_H22f zenon_H16f zenon_H16d zenon_H1a7 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H327 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H3ec zenon_H13 zenon_H14 zenon_H349 zenon_H15e zenon_H2ea zenon_H2d4 zenon_H341 zenon_H324 zenon_H2ff zenon_H2e0 zenon_H2db zenon_H13b zenon_H14e zenon_H210. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.40/51.62 apply (zenon_L116_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.40/51.62 apply (zenon_L117_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.40/51.62 apply (zenon_L118_); trivial. % 51.40/51.62 apply (zenon_L753_); trivial. % 51.40/51.62 (* end of lemma zenon_L754_ *) % 51.40/51.62 assert (zenon_L755_ : ((h4 (e13)) = (e23)) -> ((op1 (e13) (e10)) = (e13)) -> (~((e23) = (h4 (op1 (e13) (e10))))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H2ea zenon_H66 zenon_H3f2. % 51.40/51.62 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H3f3 | zenon_intro zenon_H3f4 ]. % 51.40/51.62 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((e23) = (h4 (op1 (e13) (e10))))). % 51.40/51.62 intro zenon_D_pnotp. % 51.40/51.62 apply zenon_H3f2. % 51.40/51.62 rewrite <- zenon_D_pnotp. % 51.40/51.62 exact zenon_H3f3. % 51.40/51.62 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3f4]. % 51.40/51.62 cut (((h4 (op1 (e13) (e10))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H3f5]. % 51.40/51.62 congruence. % 51.40/51.62 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e13) (e10))) = (e23))). % 51.40/51.62 intro zenon_D_pnotp. % 51.40/51.62 apply zenon_H3f5. % 51.40/51.62 rewrite <- zenon_D_pnotp. % 51.40/51.62 exact zenon_H2ea. % 51.40/51.62 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H14c]. % 51.40/51.62 cut (((h4 (e13)) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3f6]. % 51.40/51.62 congruence. % 51.40/51.62 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H3f3 | zenon_intro zenon_H3f4 ]. % 51.40/51.62 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((h4 (e13)) = (h4 (op1 (e13) (e10))))). % 51.40/51.62 intro zenon_D_pnotp. % 51.40/51.62 apply zenon_H3f6. % 51.40/51.62 rewrite <- zenon_D_pnotp. % 51.40/51.62 exact zenon_H3f3. % 51.40/51.62 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3f4]. % 51.40/51.62 cut (((h4 (op1 (e13) (e10))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3f7]. % 51.40/51.62 congruence. % 51.40/51.62 cut (((op1 (e13) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_He9]. % 51.40/51.62 congruence. % 51.40/51.62 exact (zenon_He9 zenon_H66). % 51.40/51.62 apply zenon_H3f4. apply refl_equal. % 51.40/51.62 apply zenon_H3f4. apply refl_equal. % 51.40/51.62 apply zenon_H14c. apply refl_equal. % 51.40/51.62 apply zenon_H3f4. apply refl_equal. % 51.40/51.62 apply zenon_H3f4. apply refl_equal. % 51.40/51.62 (* end of lemma zenon_L755_ *) % 51.40/51.62 assert (zenon_L756_ : ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((op1 (e13) (e10)) = (e13)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H66 zenon_H3f8. % 51.40/51.62 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H3fa ]. % 51.40/51.62 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))). % 51.40/51.62 intro zenon_D_pnotp. % 51.40/51.62 apply zenon_H3f8. % 51.40/51.62 rewrite <- zenon_D_pnotp. % 51.40/51.62 exact zenon_H3f9. % 51.40/51.62 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3fa]. % 51.40/51.62 cut (((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3fb]. % 51.40/51.62 congruence. % 51.40/51.62 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))). % 51.40/51.62 intro zenon_D_pnotp. % 51.40/51.62 apply zenon_H3fb. % 51.40/51.62 rewrite <- zenon_D_pnotp. % 51.40/51.62 exact zenon_H1cd. % 51.40/51.62 cut (((e23) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3f2]. % 51.40/51.62 cut (((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3fc]. % 51.40/51.62 congruence. % 51.40/51.62 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H3f9 | zenon_intro zenon_H3fa ]. % 51.40/51.62 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))). % 51.40/51.62 intro zenon_D_pnotp. % 51.40/51.62 apply zenon_H3fc. % 51.40/51.62 rewrite <- zenon_D_pnotp. % 51.40/51.62 exact zenon_H3f9. % 51.40/51.62 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3fa]. % 51.40/51.62 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H3fd]. % 51.40/51.62 congruence. % 51.40/51.62 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 51.40/51.62 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H399]. % 51.40/51.62 congruence. % 51.40/51.62 exact (zenon_H399 zenon_H2ea). % 51.40/51.62 apply (zenon_L1_); trivial. % 51.40/51.62 apply zenon_H3fa. apply refl_equal. % 51.40/51.62 apply zenon_H3fa. apply refl_equal. % 51.40/51.62 apply (zenon_L755_); trivial. % 51.40/51.62 apply zenon_H3fa. apply refl_equal. % 51.40/51.62 apply zenon_H3fa. apply refl_equal. % 51.40/51.62 (* end of lemma zenon_L756_ *) % 51.40/51.62 assert (zenon_L757_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e12)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 51.40/51.62 do 0 intro. intros zenon_H31b zenon_H1c zenon_Hb8 zenon_H19 zenon_H113 zenon_Hf1 zenon_Hf0 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H31b); [ zenon_intro zenon_Hb9 | zenon_intro zenon_H31c ]. % 51.40/51.62 apply (zenon_L39_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H31c); [ zenon_intro zenon_H114 | zenon_intro zenon_H31d ]. % 51.40/51.62 apply (zenon_L82_); trivial. % 51.40/51.62 apply (zenon_or_s _ _ zenon_H31d); [ zenon_intro zenon_He8 | zenon_intro zenon_H66 ]. % 51.40/51.62 apply (zenon_L64_); trivial. % 51.40/51.62 apply (zenon_L756_); trivial. % 51.40/51.62 (* end of lemma zenon_L757_ *) % 51.40/51.62 assert (zenon_L758_ : (((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)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e13)) = (e10)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_Hc8 zenon_H3d zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_Hea zenon_H50 zenon_H41 zenon_He1 zenon_Hcf zenon_Hc2 zenon_H8c zenon_Hde zenon_H35 zenon_Hbe zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_Hf0 zenon_H113 zenon_H19 zenon_Hb8 zenon_H31b zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.63 apply (zenon_L408_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.63 apply (zenon_L308_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.63 apply (zenon_L757_); trivial. % 51.40/51.63 apply (zenon_L46_); trivial. % 51.40/51.63 (* end of lemma zenon_L758_ *) % 51.40/51.63 assert (zenon_L759_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hcf zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_Hbe zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H8c zenon_Hde zenon_H3d zenon_H19. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.63 apply (zenon_L756_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.63 apply (zenon_L40_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.63 apply (zenon_L372_); trivial. % 51.40/51.63 apply (zenon_L37_); trivial. % 51.40/51.63 (* end of lemma zenon_L759_ *) % 51.40/51.63 assert (zenon_L760_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H3d zenon_Hde zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_Hcf zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.63 apply (zenon_L39_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.63 apply (zenon_L759_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.63 apply (zenon_L41_); trivial. % 51.40/51.63 apply (zenon_L24_); trivial. % 51.40/51.63 (* end of lemma zenon_L760_ *) % 51.40/51.63 assert (zenon_L761_ : ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e11))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hbe zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_H8c zenon_He8 zenon_H4b zenon_Hcf zenon_Hab zenon_H1c zenon_H2c zenon_H95 zenon_H54 zenon_H9e zenon_H49 zenon_Hda zenon_H311 zenon_H62 zenon_H123 zenon_H10e zenon_Hb5 zenon_H30d zenon_Hde zenon_H7d zenon_H35 zenon_H90 zenon_Hd3 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_H3d zenon_H19. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.63 apply (zenon_L756_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.63 apply (zenon_L40_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.63 apply (zenon_L335_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H121 | zenon_intro zenon_H312 ]. % 51.40/51.63 apply (zenon_L88_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H10a | zenon_intro zenon_H313 ]. % 51.40/51.63 apply (zenon_L347_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H7c | zenon_intro zenon_He2 ]. % 51.40/51.63 apply (zenon_L341_); trivial. % 51.40/51.63 apply (zenon_L760_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.63 apply (zenon_L346_); trivial. % 51.40/51.63 apply (zenon_L37_); trivial. % 51.40/51.63 apply (zenon_L37_); trivial. % 51.40/51.63 (* end of lemma zenon_L761_ *) % 51.40/51.63 assert (zenon_L762_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e12) (e13)) = (e10)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H19 zenon_H3d zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_H90 zenon_H35 zenon_H7d zenon_Hde zenon_H30d zenon_Hb5 zenon_H10e zenon_H123 zenon_H62 zenon_H311 zenon_H9e zenon_H54 zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_H8c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_Hbe zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.63 apply (zenon_L761_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.63 apply (zenon_L34_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.63 apply (zenon_L45_); trivial. % 51.40/51.63 apply (zenon_L46_); trivial. % 51.40/51.63 (* end of lemma zenon_L762_ *) % 51.40/51.63 assert (zenon_L763_ : (((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)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_Hbe zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_H42 zenon_H4b zenon_Hcf zenon_H95 zenon_H54 zenon_H9e zenon_H311 zenon_H62 zenon_H123 zenon_H10e zenon_Hb5 zenon_H30d zenon_Hde zenon_H7d zenon_H90 zenon_H3d zenon_H8c zenon_Hc2 zenon_H35 zenon_Hc8 zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_Hf0 zenon_H113 zenon_H19 zenon_Hb8 zenon_H31b zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.63 apply (zenon_L762_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.63 apply (zenon_L309_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.63 apply (zenon_L757_); trivial. % 51.40/51.63 apply (zenon_L46_); trivial. % 51.40/51.63 (* end of lemma zenon_L763_ *) % 51.40/51.63 assert (zenon_L764_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hda zenon_H1c zenon_H2c zenon_H31b zenon_Hb8 zenon_H113 zenon_Hf0 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_Hc8 zenon_H35 zenon_Hc2 zenon_H3d zenon_H90 zenon_H7d zenon_Hde zenon_H30d zenon_Hb5 zenon_H10e zenon_H123 zenon_H311 zenon_H9e zenon_H54 zenon_H95 zenon_Hcf zenon_H4b zenon_H42 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_Hbe zenon_Hab zenon_Hd3 zenon_H327 zenon_H19 zenon_H8c. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.63 apply (zenon_L47_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.63 apply (zenon_L758_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.63 apply (zenon_L763_); trivial. % 51.40/51.63 apply (zenon_L24_); trivial. % 51.40/51.63 (* end of lemma zenon_L764_ *) % 51.40/51.63 assert (zenon_L765_ : (((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)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_H42 zenon_H4b zenon_Hcf zenon_H95 zenon_H54 zenon_H9e zenon_H311 zenon_H123 zenon_H10e zenon_Hb5 zenon_H30d zenon_Hde zenon_H7d zenon_H90 zenon_H3d zenon_H35 zenon_Hc8 zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_Hf0 zenon_H113 zenon_Hb8 zenon_H31b zenon_H2c zenon_Hda zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.63 apply (zenon_L39_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.63 apply (zenon_L764_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.63 apply (zenon_L41_); trivial. % 51.40/51.63 apply (zenon_L24_); trivial. % 51.40/51.63 (* end of lemma zenon_L765_ *) % 51.40/51.63 assert (zenon_L766_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((e10) = (e11))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hcf zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_H8c zenon_H1c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Ha3 zenon_Hcb zenon_H3d zenon_H19. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.63 apply (zenon_L756_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.63 apply (zenon_L42_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.63 apply (zenon_L43_); trivial. % 51.40/51.63 apply (zenon_L37_); trivial. % 51.40/51.63 (* end of lemma zenon_L766_ *) % 51.40/51.63 assert (zenon_L767_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e10) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hfb zenon_H23 zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_Hcf zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_Hde zenon_H3d zenon_Hb8 zenon_Hc8 zenon_Hcb zenon_H45 zenon_H46 zenon_H108 zenon_Hf8 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.63 apply (zenon_L317_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.63 apply (zenon_L328_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.63 apply (zenon_L328_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.63 apply (zenon_L13_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.63 apply (zenon_L766_); trivial. % 51.40/51.63 apply (zenon_L760_); trivial. % 51.40/51.63 apply (zenon_L756_); trivial. % 51.40/51.63 (* end of lemma zenon_L767_ *) % 51.40/51.63 assert (zenon_L768_ : (((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)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e11))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e12)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_Hb0 zenon_Hc2 zenon_Hcf zenon_H8c zenon_H42 zenon_Hc8 zenon_H131 zenon_H108 zenon_H128 zenon_H12c zenon_He1 zenon_Hec zenon_Hf3 zenon_Hcb zenon_He2 zenon_H62 zenon_H7d zenon_Hde zenon_H4b zenon_Hb5 zenon_H2db zenon_He6 zenon_H324 zenon_H95 zenon_H54 zenon_H9e zenon_H90 zenon_H3d zenon_H35 zenon_Hbe zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_Hf0 zenon_H113 zenon_H19 zenon_Hb8 zenon_H31b zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.63 apply (zenon_L414_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.63 apply (zenon_L308_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.63 apply (zenon_L757_); trivial. % 51.40/51.63 apply (zenon_L46_); trivial. % 51.40/51.63 (* end of lemma zenon_L768_ *) % 51.40/51.63 assert (zenon_L769_ : ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (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) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H126 zenon_Hda zenon_H1c zenon_H2c zenon_H31b zenon_Hb8 zenon_H113 zenon_Hf0 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_Hbe zenon_H35 zenon_H3d zenon_H90 zenon_H9e zenon_H54 zenon_H95 zenon_H324 zenon_He6 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hde zenon_H7d zenon_He2 zenon_Hcb zenon_Hf3 zenon_Hec zenon_He1 zenon_H12c zenon_H128 zenon_H108 zenon_H131 zenon_Hc8 zenon_H42 zenon_Hcf zenon_Hc2 zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H327 zenon_H19 zenon_H8c. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.63 apply (zenon_L47_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.63 apply (zenon_L303_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.63 apply (zenon_L768_); trivial. % 51.40/51.63 apply (zenon_L24_); trivial. % 51.40/51.63 (* end of lemma zenon_L769_ *) % 51.40/51.63 assert (zenon_L770_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hcf zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_H131 zenon_Hbe zenon_H321 zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_H1c zenon_Hc2 zenon_Hf3 zenon_Hcb zenon_Hde zenon_H8c zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.63 apply (zenon_L756_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.63 apply (zenon_L40_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.63 apply (zenon_L417_); trivial. % 51.40/51.63 apply (zenon_L37_); trivial. % 51.40/51.63 (* end of lemma zenon_L770_ *) % 51.40/51.63 assert (zenon_L771_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (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 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H19 zenon_H3d zenon_Hb5 zenon_H4b zenon_H90 zenon_H35 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_H8c zenon_Hde zenon_Hcb zenon_Hf3 zenon_Hc2 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H128 zenon_H108 zenon_H321 zenon_Hbe zenon_H131 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.63 apply (zenon_L770_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.63 apply (zenon_L34_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.63 apply (zenon_L45_); trivial. % 51.40/51.63 apply (zenon_L46_); trivial. % 51.40/51.63 (* end of lemma zenon_L771_ *) % 51.40/51.63 assert (zenon_L772_ : (((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)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (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) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_Hcf zenon_H131 zenon_Hbe zenon_H321 zenon_H108 zenon_H128 zenon_H9e zenon_H12c zenon_He1 zenon_Hec zenon_Hf3 zenon_Hcb zenon_Hde zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H90 zenon_H4b zenon_Hb5 zenon_H3d zenon_H8c zenon_Hc2 zenon_H35 zenon_Hc8 zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_Hf0 zenon_H113 zenon_H19 zenon_Hb8 zenon_H31b zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.63 apply (zenon_L771_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.63 apply (zenon_L309_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.63 apply (zenon_L757_); trivial. % 51.40/51.63 apply (zenon_L46_); trivial. % 51.40/51.63 (* end of lemma zenon_L772_ *) % 51.40/51.63 assert (zenon_L773_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((e10) = (e11))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H324 zenon_He6 zenon_H2db zenon_H50 zenon_Hda zenon_H2c zenon_H31b zenon_Hb8 zenon_H113 zenon_Hf0 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_Hc8 zenon_H35 zenon_H8c zenon_H3d zenon_Hb5 zenon_H4b zenon_H90 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_Hde zenon_Hcb zenon_Hf3 zenon_Hec zenon_He1 zenon_H12c zenon_H9e zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_Hcf zenon_Hab zenon_Hd3 zenon_H327 zenon_H1c zenon_H19 zenon_Hc2. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.40/51.63 apply (zenon_L56_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.40/51.63 apply (zenon_L303_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.40/51.63 apply (zenon_L772_); trivial. % 51.40/51.63 apply (zenon_L41_); trivial. % 51.40/51.63 (* end of lemma zenon_L773_ *) % 51.40/51.63 assert (zenon_L774_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e10) (e10)) = (e10)) -> (~((e12) = (e13))) -> ((op1 (e11) (e10)) = (e12)) -> (~((e11) = (e13))) -> ((op1 (e12) (e10)) = (e11)) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hfb zenon_H42 zenon_H23 zenon_H4b zenon_H34 zenon_H3d zenon_H10a zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.63 apply (zenon_L317_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.63 apply (zenon_L86_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.63 apply (zenon_L421_); trivial. % 51.40/51.63 apply (zenon_L756_); trivial. % 51.40/51.63 (* end of lemma zenon_L774_ *) % 51.40/51.63 assert (zenon_L775_ : (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H2db zenon_H126 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_Hbe zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_Hc8 zenon_Hb8 zenon_H42 zenon_Hc2 zenon_He8 zenon_H4b zenon_Hcf zenon_H95 zenon_H54 zenon_H9e zenon_H311 zenon_H123 zenon_H10e zenon_Hb5 zenon_H30d zenon_Hde zenon_H7d zenon_H35 zenon_H90 zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_H3d zenon_H19 zenon_H8c. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.63 apply (zenon_L47_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.63 apply (zenon_L303_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.63 apply (zenon_L762_); trivial. % 51.40/51.63 apply (zenon_L24_); trivial. % 51.40/51.63 (* end of lemma zenon_L775_ *) % 51.40/51.63 assert (zenon_L776_ : (~((e11) = (e13))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H3d zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_H90 zenon_H35 zenon_H7d zenon_Hde zenon_H30d zenon_Hb5 zenon_H10e zenon_H123 zenon_H311 zenon_H9e zenon_H54 zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H2c zenon_Hda zenon_H126 zenon_H2db zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.63 apply (zenon_L39_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.63 apply (zenon_L775_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.63 apply (zenon_L41_); trivial. % 51.40/51.63 apply (zenon_L24_); trivial. % 51.40/51.63 (* end of lemma zenon_L776_ *) % 51.40/51.63 assert (zenon_L777_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e13) (e10)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((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))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_Hff zenon_He8 zenon_Hf8 zenon_Hb0 zenon_Hea zenon_H9e zenon_Hb5 zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hc8 zenon_Hb8 zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_H35 zenon_H90 zenon_Hc2 zenon_H19 zenon_H8c zenon_H2e0 zenon_H2db zenon_H95 zenon_H311 zenon_H123 zenon_H10e zenon_H30d zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_H23 zenon_Hfb zenon_H3d zenon_H11a zenon_Hde zenon_H4b zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.63 apply (zenon_L317_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.63 apply (zenon_L317_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.63 apply (zenon_L12_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.63 apply (zenon_L283_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.63 apply (zenon_L776_); trivial. % 51.40/51.63 apply (zenon_L749_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.63 apply (zenon_L352_); trivial. % 51.40/51.63 apply (zenon_L57_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.63 apply (zenon_L427_); trivial. % 51.40/51.63 apply (zenon_L335_); trivial. % 51.40/51.63 (* end of lemma zenon_L777_ *) % 51.40/51.63 assert (zenon_L778_ : (((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)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_H4b zenon_Hde zenon_H11a zenon_H3d zenon_Hfb zenon_H23 zenon_H30d zenon_H10e zenon_H123 zenon_H311 zenon_H95 zenon_H2db zenon_H2e0 zenon_H8c zenon_Hc2 zenon_H90 zenon_Hcf zenon_H42 zenon_H7d zenon_H54 zenon_He1 zenon_Hc8 zenon_Hf3 zenon_Hec zenon_Hcb zenon_H45 zenon_Hb5 zenon_H9e zenon_Hea zenon_Hb0 zenon_Hf8 zenon_Hff zenon_H35 zenon_Hbe zenon_H3f8 zenon_H2ea zenon_H14 zenon_H13 zenon_H1cd zenon_Hf0 zenon_H113 zenon_H19 zenon_Hb8 zenon_H31b zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.63 apply (zenon_L777_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.63 apply (zenon_L308_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.63 apply (zenon_L757_); trivial. % 51.40/51.63 apply (zenon_L46_); trivial. % 51.40/51.63 (* end of lemma zenon_L778_ *) % 51.40/51.63 assert (zenon_L779_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((op2 (e23) (e20)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.63 do 0 intro. intros zenon_H13b zenon_H31b zenon_H1cd zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_H2e0 zenon_H2db zenon_H311 zenon_H30d zenon_H327 zenon_H324 zenon_H2d4 zenon_H2ba zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.63 apply (zenon_L11_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.63 apply (zenon_L765_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.40/51.63 apply (zenon_L765_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.40/51.63 apply (zenon_L299_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.40/51.63 apply (zenon_L766_); trivial. % 51.40/51.63 apply (zenon_L760_); trivial. % 51.40/51.63 apply (zenon_L756_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.40/51.63 apply (zenon_L73_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.40/51.63 apply (zenon_L317_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.40/51.63 apply (zenon_L767_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.63 apply (zenon_L317_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.63 apply (zenon_L328_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.63 apply (zenon_L74_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.63 apply (zenon_L283_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.63 apply (zenon_L39_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.63 apply (zenon_L769_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.63 apply (zenon_L41_); trivial. % 51.40/51.63 apply (zenon_L24_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.63 apply (zenon_L39_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.63 apply (zenon_L773_); trivial. % 51.40/51.63 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.64 apply (zenon_L41_); trivial. % 51.40/51.64 apply (zenon_L24_); trivial. % 51.40/51.64 apply (zenon_L756_); trivial. % 51.40/51.64 apply (zenon_L335_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.40/51.64 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.40/51.64 apply (zenon_L7_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.40/51.64 apply (zenon_L774_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.40/51.64 apply (zenon_L75_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.40/51.64 apply (zenon_L317_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H33 | zenon_intro zenon_H2e2 ]. % 51.40/51.64 apply (zenon_L81_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H2e2); [ zenon_intro zenon_H2c2 | zenon_intro zenon_H2e3 ]. % 51.40/51.64 apply (zenon_L283_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H2e3); [ zenon_intro zenon_H126 | zenon_intro zenon_H50 ]. % 51.40/51.64 apply (zenon_L776_); trivial. % 51.40/51.64 apply (zenon_L408_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.40/51.64 apply (zenon_L421_); trivial. % 51.40/51.64 apply (zenon_L57_); trivial. % 51.40/51.64 apply (zenon_L82_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.40/51.64 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.64 apply (zenon_L39_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.64 apply (zenon_L778_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.64 apply (zenon_L41_); trivial. % 51.40/51.64 apply (zenon_L24_); trivial. % 51.40/51.64 apply (zenon_L85_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.40/51.64 apply (zenon_L4_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.40/51.64 apply (zenon_L109_); trivial. % 51.40/51.64 apply (zenon_L47_); trivial. % 51.40/51.64 (* end of lemma zenon_L779_ *) % 51.40/51.64 assert (zenon_L780_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.64 do 0 intro. intros zenon_H21f zenon_H1fd zenon_H14e zenon_H217 zenon_H262 zenon_H176 zenon_H175 zenon_H15e zenon_H13b zenon_H31b zenon_H13 zenon_H14 zenon_H2ea zenon_H3f8 zenon_H2e0 zenon_H2db zenon_H311 zenon_H30d zenon_H327 zenon_H324 zenon_H2d4 zenon_H2ba zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H21f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H220 ]. % 51.40/51.64 apply (zenon_L151_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H220); [ zenon_intro zenon_H218 | zenon_intro zenon_H221 ]. % 51.40/51.64 apply (zenon_L156_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H221); [ zenon_intro zenon_H21c | zenon_intro zenon_H1cd ]. % 51.40/51.64 apply (zenon_L197_); trivial. % 51.40/51.64 apply (zenon_L779_); trivial. % 51.40/51.64 (* end of lemma zenon_L780_ *) % 51.40/51.64 assert (zenon_L781_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> ((op2 (e20) (e20)) = (e20)) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e21))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.64 do 0 intro. intros zenon_H2a5 zenon_H2b7 zenon_H1ac zenon_H24b zenon_H209 zenon_H14 zenon_H23c zenon_H21b zenon_H2b6 zenon_H259 zenon_H13c zenon_H24e zenon_H240 zenon_H214 zenon_H1ec zenon_H1e6 zenon_H1cc zenon_H1f3 zenon_H217 zenon_H1fd zenon_H21f zenon_H1a7 zenon_H15e zenon_H18e zenon_H187 zenon_H1fa zenon_H210 zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H245 zenon_H205 zenon_H19b zenon_H16f zenon_H22f zenon_H254 zenon_H1f7 zenon_H258 zenon_H262 zenon_H13b zenon_H31b zenon_H13 zenon_H2ea zenon_H3f8 zenon_H2e0 zenon_H2db zenon_H311 zenon_H30d zenon_H327 zenon_H324 zenon_H2d4 zenon_H2ba zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H36d zenon_H36a zenon_H164 zenon_H22b zenon_H222 zenon_H15d zenon_H28e zenon_H168 zenon_H28d zenon_H195 zenon_H14e. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.40/51.64 apply (zenon_L259_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.40/51.64 apply (zenon_L280_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.40/51.64 apply (zenon_L116_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.40/51.64 apply (zenon_L117_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.40/51.64 apply (zenon_L118_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.40/51.64 apply (zenon_L116_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.40/51.64 apply (zenon_L533_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.40/51.64 apply (zenon_L780_); trivial. % 51.40/51.64 apply (zenon_L534_); trivial. % 51.40/51.64 apply (zenon_L234_); trivial. % 51.40/51.64 (* end of lemma zenon_L781_ *) % 51.40/51.64 assert (zenon_L782_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e20)) = (e21)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e20) = (e23))) -> ((op2 (e20) (e22)) = (e20)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.40/51.64 do 0 intro. intros zenon_H28d zenon_H164 zenon_H168 zenon_H28e zenon_H15d zenon_H16d zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2ba zenon_H2d4 zenon_H324 zenon_H327 zenon_H30d zenon_H311 zenon_H2db zenon_H2e0 zenon_H3f8 zenon_H2ea zenon_H13 zenon_H31b zenon_H13b zenon_H262 zenon_H258 zenon_H14e zenon_H1f7 zenon_H254 zenon_H22f zenon_H16f zenon_H245 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H21b zenon_H23c zenon_H209 zenon_H24b zenon_H210 zenon_H1fa zenon_H1a7 zenon_H21f zenon_H1fd zenon_H217 zenon_H1f3 zenon_H1cc zenon_H1e6 zenon_H1ec zenon_H214 zenon_H240 zenon_H24e zenon_H237 zenon_H259 zenon_H205 zenon_H156 zenon_H19b zenon_H1ac zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H195. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.40/51.64 apply (zenon_L116_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.40/51.64 apply (zenon_L117_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.40/51.64 apply (zenon_L118_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.40/51.64 apply (zenon_L116_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.40/51.64 apply (zenon_L120_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.40/51.64 apply (zenon_L780_); trivial. % 51.40/51.64 apply (zenon_L195_); trivial. % 51.40/51.64 (* end of lemma zenon_L782_ *) % 51.40/51.64 assert (zenon_L783_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.64 do 0 intro. intros zenon_H222 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2ba zenon_H2d4 zenon_H324 zenon_H327 zenon_H30d zenon_H311 zenon_H2db zenon_H2e0 zenon_H3f8 zenon_H2ea zenon_H13 zenon_H31b zenon_H13b zenon_H209 zenon_H1fd zenon_H214 zenon_H210 zenon_H254 zenon_H266 zenon_H285 zenon_H27c zenon_H203 zenon_H14 zenon_H280 zenon_H27f zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H22f zenon_H16f zenon_H205 zenon_H1ac zenon_H1fa zenon_H283 zenon_H1f7 zenon_H14e. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.40/51.64 apply (zenon_L779_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.40/51.64 apply (zenon_L155_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.40/51.64 apply (zenon_L249_); trivial. % 51.40/51.64 apply (zenon_L149_); trivial. % 51.40/51.64 (* end of lemma zenon_L783_ *) % 51.40/51.64 assert (zenon_L784_ : (~((e21) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.64 do 0 intro. intros zenon_H1f7 zenon_H283 zenon_H1fa zenon_H1ac zenon_H205 zenon_H16f zenon_H22f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H27f zenon_H280 zenon_H27c zenon_H285 zenon_H266 zenon_H254 zenon_H214 zenon_H1fd zenon_H13b zenon_H31b zenon_H13 zenon_H2ea zenon_H3f8 zenon_H2e0 zenon_H2db zenon_H311 zenon_H30d zenon_H327 zenon_H324 zenon_H2d4 zenon_H2ba zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H222 zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.40/51.64 apply (zenon_L151_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.40/51.64 apply (zenon_L783_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.40/51.64 apply (zenon_L153_); trivial. % 51.40/51.64 apply (zenon_L154_); trivial. % 51.40/51.64 (* end of lemma zenon_L784_ *) % 51.40/51.64 assert (zenon_L785_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e23) (e22)) = (e23)) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.40/51.64 do 0 intro. intros zenon_H273 zenon_H210 zenon_H14e zenon_H14 zenon_H209 zenon_H222 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2ba zenon_H2d4 zenon_H324 zenon_H327 zenon_H30d zenon_H311 zenon_H2db zenon_H2e0 zenon_H3f8 zenon_H2ea zenon_H13 zenon_H31b zenon_H13b zenon_H1fd zenon_H214 zenon_H254 zenon_H285 zenon_H27c zenon_H280 zenon_H27f zenon_H1ec zenon_H22f zenon_H16f zenon_H205 zenon_H1ac zenon_H1fa zenon_H283 zenon_H1f7 zenon_H26d zenon_H203 zenon_H1bc zenon_H1bd zenon_H226 zenon_H225 zenon_H1d7 zenon_H267 zenon_H17f zenon_H1c9 zenon_H1b1 zenon_H21d zenon_H175 zenon_H195. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H266 | zenon_intro zenon_H274 ]. % 51.40/51.64 apply (zenon_L784_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H26e | zenon_intro zenon_H275 ]. % 51.40/51.64 apply (zenon_L205_); trivial. % 51.40/51.64 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H176 | zenon_intro zenon_H252 ]. % 51.40/51.64 apply (zenon_L161_); trivial. % 51.40/51.64 apply (zenon_L206_); trivial. % 51.40/51.64 (* end of lemma zenon_L785_ *) % 51.40/51.64 assert (zenon_L786_ : ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e20) = (e21))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H21c zenon_H1d7 zenon_H267 zenon_H17f zenon_H1ec zenon_H175 zenon_H195 zenon_H273 zenon_H210 zenon_H14 zenon_H209 zenon_H222 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2ba zenon_H2d4 zenon_H324 zenon_H327 zenon_H30d zenon_H311 zenon_H2db zenon_H2e0 zenon_H3f8 zenon_H2ea zenon_H13 zenon_H31b zenon_H13b zenon_H1fd zenon_H214 zenon_H254 zenon_H285 zenon_H27c zenon_H280 zenon_H27f zenon_H22f zenon_H16f zenon_H205 zenon_H1ac zenon_H1fa zenon_H283 zenon_H26d zenon_H203 zenon_H1bd zenon_H226 zenon_H225 zenon_H1c9 zenon_H1b1 zenon_H1f7 zenon_H14e. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.40/51.65 apply (zenon_L192_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.40/51.65 apply (zenon_L152_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.40/51.65 apply (zenon_L132_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.40/51.65 apply (zenon_L785_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.40/51.65 apply (zenon_L202_); trivial. % 51.40/51.65 apply (zenon_L149_); trivial. % 51.40/51.65 apply (zenon_L149_); trivial. % 51.40/51.65 (* end of lemma zenon_L786_ *) % 51.40/51.65 assert (zenon_L787_ : ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H15e zenon_H18e zenon_H187 zenon_H19b zenon_H16d zenon_H1a7 zenon_H1f7 zenon_H1b1 zenon_H225 zenon_H226 zenon_H1bd zenon_H203 zenon_H26d zenon_H283 zenon_H1fa zenon_H1ac zenon_H205 zenon_H16f zenon_H22f zenon_H27f zenon_H280 zenon_H27c zenon_H285 zenon_H254 zenon_H214 zenon_H1fd zenon_H13b zenon_H31b zenon_H13 zenon_H2ea zenon_H3f8 zenon_H2e0 zenon_H2db zenon_H311 zenon_H30d zenon_H327 zenon_H324 zenon_H2d4 zenon_H2ba zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H222 zenon_H209 zenon_H14 zenon_H273 zenon_H195 zenon_H175 zenon_H1ec zenon_H17f zenon_H267 zenon_H1d7 zenon_H21c zenon_H14e zenon_H210. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.40/51.65 apply (zenon_L183_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.40/51.65 apply (zenon_L130_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.40/51.65 apply (zenon_L786_); trivial. % 51.40/51.65 apply (zenon_L154_); trivial. % 51.40/51.65 (* end of lemma zenon_L787_ *) % 51.40/51.65 assert (zenon_L788_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H222 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2ba zenon_H2d4 zenon_H324 zenon_H327 zenon_H30d zenon_H311 zenon_H2db zenon_H2e0 zenon_H3f8 zenon_H2ea zenon_H13 zenon_H31b zenon_H13b zenon_H285 zenon_H210 zenon_H273 zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H26d zenon_H203 zenon_H19f zenon_H14 zenon_H19e zenon_H15e zenon_H1bd zenon_H1b1 zenon_H19b zenon_H187 zenon_H18e zenon_H27c zenon_H1f3 zenon_H280 zenon_H27f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H283 zenon_H1ac zenon_H1fa zenon_H1f7 zenon_H14e. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.40/51.65 apply (zenon_L779_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.40/51.65 apply (zenon_L152_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.40/51.65 apply (zenon_L218_); trivial. % 51.40/51.65 apply (zenon_L149_); trivial. % 51.40/51.65 (* end of lemma zenon_L788_ *) % 51.40/51.65 assert (zenon_L789_ : (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e20) = (e21))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e10)) = (e11))\/(((op1 (e13) (e10)) = (e12))\/((op1 (e13) (e10)) = (e13))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H2af zenon_H262 zenon_H217 zenon_H21f zenon_H21c zenon_H21b zenon_H16d zenon_H1a7 zenon_H225 zenon_H214 zenon_H1fd zenon_H209 zenon_H168 zenon_H230 zenon_H14e zenon_H1f7 zenon_H1fa zenon_H1ac zenon_H283 zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H27f zenon_H280 zenon_H1f3 zenon_H27c zenon_H187 zenon_H19b zenon_H1b1 zenon_H1bd zenon_H19f zenon_H203 zenon_H26d zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H273 zenon_H210 zenon_H285 zenon_H13b zenon_H31b zenon_H13 zenon_H2ea zenon_H3f8 zenon_H2e0 zenon_H2db zenon_H311 zenon_H30d zenon_H327 zenon_H324 zenon_H2d4 zenon_H2ba zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H222 zenon_H15e zenon_H14 zenon_H18e. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H2af); [ zenon_intro zenon_H176 | zenon_intro zenon_H2b2 ]. % 51.40/51.65 apply (zenon_L780_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H2b2); [ zenon_intro zenon_H226 | zenon_intro zenon_H2b3 ]. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H169 | zenon_intro zenon_H233 ]. % 51.40/51.65 apply (zenon_L118_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H17f | zenon_intro zenon_H234 ]. % 51.40/51.65 apply (zenon_L787_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H19e | zenon_intro zenon_H1d8 ]. % 51.40/51.65 apply (zenon_L788_); trivial. % 51.40/51.65 apply (zenon_L157_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H2b3); [ zenon_intro zenon_H19e | zenon_intro zenon_H18d ]. % 51.40/51.65 apply (zenon_L788_); trivial. % 51.40/51.65 apply (zenon_L125_); trivial. % 51.40/51.65 (* end of lemma zenon_L789_ *) % 51.40/51.65 assert (zenon_L790_ : (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((op1 (e13) (e11)) = (e10)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 51.40/51.65 do 0 intro. intros zenon_H3fe zenon_H13 zenon_Hbe zenon_H2e7 zenon_H2ea. % 51.40/51.65 cut (((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) = ((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H3fe. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H13. % 51.40/51.65 cut (((op2 (e23) (op2 (e23) (e23))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3ff]. % 51.40/51.65 cut (((h4 (e10)) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H400]. % 51.40/51.65 congruence. % 51.40/51.65 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H401 | zenon_intro zenon_H402 ]. % 51.40/51.65 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((h4 (e10)) = (h4 (op1 (e13) (e11))))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H400. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H401. % 51.40/51.65 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H402]. % 51.40/51.65 cut (((h4 (op1 (e13) (e11))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H403]. % 51.40/51.65 congruence. % 51.40/51.65 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H404]. % 51.40/51.65 congruence. % 51.40/51.65 exact (zenon_H404 zenon_Hbe). % 51.40/51.65 apply zenon_H402. apply refl_equal. % 51.40/51.65 apply zenon_H402. apply refl_equal. % 51.40/51.65 cut (((op2 (e23) (e23)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H405]. % 51.40/51.65 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H35d]. % 51.40/51.65 congruence. % 51.40/51.65 apply zenon_H35d. apply sym_equal. exact zenon_H2ea. % 51.40/51.65 apply zenon_H405. apply sym_equal. exact zenon_H2e7. % 51.40/51.65 (* end of lemma zenon_L790_ *) % 51.40/51.65 assert (zenon_L791_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.65 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H2ea zenon_H2e7 zenon_H13 zenon_H3fe zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.65 apply (zenon_L39_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.65 apply (zenon_L790_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.65 apply (zenon_L41_); trivial. % 51.40/51.65 apply (zenon_L24_); trivial. % 51.40/51.65 (* end of lemma zenon_L791_ *) % 51.40/51.65 assert (zenon_L792_ : ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e13) (e12)) = (e12)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((e22) = (h4 (op1 (e13) (e12))))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H349 zenon_Hf1 zenon_H15e zenon_H406. % 51.40/51.65 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H407 | zenon_intro zenon_H408 ]. % 51.40/51.65 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((e22) = (h4 (op1 (e13) (e12))))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H406. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H407. % 51.40/51.65 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H408]. % 51.40/51.65 cut (((h4 (op1 (e13) (e12))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H409]. % 51.40/51.65 congruence. % 51.40/51.65 cut (((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e13) (e12))) = (e22))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H409. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H349. % 51.40/51.65 cut (((op2 (op2 (e23) (op2 (e23) (e23))) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H34a]. % 51.40/51.65 cut (((h4 (e12)) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H40a]. % 51.40/51.65 congruence. % 51.40/51.65 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H407 | zenon_intro zenon_H408 ]. % 51.40/51.65 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((h4 (e12)) = (h4 (op1 (e13) (e12))))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H40a. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H407. % 51.40/51.65 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H408]. % 51.40/51.65 cut (((h4 (op1 (e13) (e12))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H40b]. % 51.40/51.65 congruence. % 51.40/51.65 cut (((op1 (e13) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H40c]. % 51.40/51.65 congruence. % 51.40/51.65 exact (zenon_H40c zenon_Hf1). % 51.40/51.65 apply zenon_H408. apply refl_equal. % 51.40/51.65 apply zenon_H408. apply refl_equal. % 51.40/51.65 apply zenon_H34a. apply sym_equal. exact zenon_H15e. % 51.40/51.65 apply zenon_H408. apply refl_equal. % 51.40/51.65 apply zenon_H408. apply refl_equal. % 51.40/51.65 (* end of lemma zenon_L792_ *) % 51.40/51.65 assert (zenon_L793_ : ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((op1 (e13) (e12)) = (e12)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_Hf1 zenon_H40d. % 51.40/51.65 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H40e | zenon_intro zenon_H40f ]. % 51.40/51.65 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H40d. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H40e. % 51.40/51.65 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H40f]. % 51.40/51.65 cut (((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H410]. % 51.40/51.65 congruence. % 51.40/51.65 cut (((op2 (e23) (e22)) = (e22)) = ((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H410. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H1d8. % 51.40/51.65 cut (((e22) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H406]. % 51.40/51.65 cut (((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H411]. % 51.40/51.65 congruence. % 51.40/51.65 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H40e | zenon_intro zenon_H40f ]. % 51.40/51.65 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))). % 51.40/51.65 intro zenon_D_pnotp. % 51.40/51.65 apply zenon_H411. % 51.40/51.65 rewrite <- zenon_D_pnotp. % 51.40/51.65 exact zenon_H40e. % 51.40/51.65 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H40f]. % 51.40/51.65 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H412]. % 51.40/51.65 congruence. % 51.40/51.65 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 51.40/51.65 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H399]. % 51.40/51.65 congruence. % 51.40/51.65 exact (zenon_H399 zenon_H2ea). % 51.40/51.65 apply (zenon_L487_); trivial. % 51.40/51.65 apply zenon_H40f. apply refl_equal. % 51.40/51.65 apply zenon_H40f. apply refl_equal. % 51.40/51.65 apply (zenon_L792_); trivial. % 51.40/51.65 apply zenon_H40f. apply refl_equal. % 51.40/51.65 apply zenon_H40f. apply refl_equal. % 51.40/51.65 (* end of lemma zenon_L793_ *) % 51.40/51.65 assert (zenon_L794_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e13)) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H327 zenon_H4b zenon_H66 zenon_H35 zenon_Hbe zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.65 apply (zenon_L57_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.65 apply (zenon_L308_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.65 apply (zenon_L793_); trivial. % 51.40/51.65 apply (zenon_L46_); trivial. % 51.40/51.65 (* end of lemma zenon_L794_ *) % 51.40/51.65 assert (zenon_L795_ : (((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)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e13) (e11)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_Hcf zenon_H4b zenon_H42 zenon_Hbe zenon_H7d zenon_H62 zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.65 apply (zenon_L349_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.65 apply (zenon_L309_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.65 apply (zenon_L793_); trivial. % 51.40/51.65 apply (zenon_L46_); trivial. % 51.40/51.65 (* end of lemma zenon_L795_ *) % 51.40/51.65 assert (zenon_L796_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H90 zenon_Hda zenon_H1c zenon_H2c zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_Hde zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_Hbe zenon_H42 zenon_H4b zenon_Hcf zenon_Hab zenon_Hd3 zenon_H327 zenon_H19 zenon_H8c. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.40/51.65 apply (zenon_L47_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.40/51.65 apply (zenon_L17_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.40/51.65 apply (zenon_L795_); trivial. % 51.40/51.65 apply (zenon_L24_); trivial. % 51.40/51.65 (* end of lemma zenon_L796_ *) % 51.40/51.65 assert (zenon_L797_ : (((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)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H327 zenon_Hd3 zenon_Hab zenon_Hcf zenon_H4b zenon_H42 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_Hde zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_Hda zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.65 apply (zenon_L39_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.65 apply (zenon_L796_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.65 apply (zenon_L41_); trivial. % 51.40/51.65 apply (zenon_L24_); trivial. % 51.40/51.65 (* end of lemma zenon_L797_ *) % 51.40/51.65 assert (zenon_L798_ : ((op1 (e13) (e11)) = (e10)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((op1 (e13) (e10)) = (e12)) -> (~((e10) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e12))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.65 do 0 intro. intros zenon_Hbe zenon_Hde zenon_H9e zenon_H54 zenon_H95 zenon_Hcf zenon_H4b zenon_He8 zenon_H8c zenon_Hc2 zenon_H42 zenon_Hb8 zenon_Hc8 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H311 zenon_H123 zenon_H3b zenon_Hfb zenon_H10e zenon_Hb5 zenon_H30d zenon_H49 zenon_H327 zenon_H7d zenon_H35 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H90 zenon_H3d zenon_H19. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.65 apply (zenon_L794_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.65 apply (zenon_L42_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.40/51.65 apply (zenon_L335_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H311); [ zenon_intro zenon_H121 | zenon_intro zenon_H312 ]. % 51.40/51.65 apply (zenon_L98_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H10a | zenon_intro zenon_H313 ]. % 51.40/51.65 apply (zenon_L347_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H7c | zenon_intro zenon_He2 ]. % 51.40/51.65 apply (zenon_L341_); trivial. % 51.40/51.65 apply (zenon_L797_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.40/51.65 apply (zenon_L672_); trivial. % 51.40/51.65 apply (zenon_L37_); trivial. % 51.40/51.65 apply (zenon_L37_); trivial. % 51.40/51.65 (* end of lemma zenon_L798_ *) % 51.40/51.65 assert (zenon_L799_ : (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H3d zenon_H90 zenon_H7d zenon_H327 zenon_H49 zenon_H30d zenon_Hb5 zenon_H10e zenon_Hfb zenon_H3b zenon_H123 zenon_H311 zenon_Hd3 zenon_Hab zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_H42 zenon_H4b zenon_Hcf zenon_H95 zenon_H54 zenon_H9e zenon_Hde zenon_Hbe zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.65 apply (zenon_L798_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.65 apply (zenon_L309_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.65 apply (zenon_L793_); trivial. % 51.40/51.65 apply (zenon_L46_); trivial. % 51.40/51.65 (* end of lemma zenon_L799_ *) % 51.40/51.65 assert (zenon_L800_ : ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H19 zenon_H8c zenon_Hbe zenon_Hde zenon_H9e zenon_H54 zenon_H95 zenon_Hcf zenon_H4b zenon_H42 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_H311 zenon_H123 zenon_H3b zenon_Hfb zenon_H10e zenon_Hb5 zenon_H30d zenon_H327 zenon_H7d zenon_H90 zenon_H3d zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.65 apply (zenon_L799_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.65 apply (zenon_L34_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.65 apply (zenon_L45_); trivial. % 51.40/51.65 apply (zenon_L46_); trivial. % 51.40/51.65 (* end of lemma zenon_L800_ *) % 51.40/51.65 assert (zenon_L801_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.65 do 0 intro. intros zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H3d zenon_H90 zenon_H7d zenon_H327 zenon_H30d zenon_Hb5 zenon_H10e zenon_Hfb zenon_H3b zenon_H123 zenon_H311 zenon_Hb0 zenon_He1 zenon_H41 zenon_Hea zenon_H42 zenon_H4b zenon_Hcf zenon_H95 zenon_H54 zenon_H9e zenon_Hde zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.65 apply (zenon_L39_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.65 apply (zenon_L800_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.65 apply (zenon_L41_); trivial. % 51.40/51.65 apply (zenon_L24_); trivial. % 51.40/51.65 (* end of lemma zenon_L801_ *) % 51.40/51.65 assert (zenon_L802_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((op1 (e11) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H327 zenon_Ha3 zenon_Hcb zenon_Hf0 zenon_Hec zenon_H19 zenon_Hc2 zenon_Hf3 zenon_H35 zenon_Hbe zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.65 apply (zenon_L65_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.65 apply (zenon_L308_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.65 apply (zenon_L793_); trivial. % 51.40/51.65 apply (zenon_L46_); trivial. % 51.40/51.65 (* end of lemma zenon_L802_ *) % 51.40/51.65 assert (zenon_L803_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e12)) = (e13)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.65 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H2c zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_H35 zenon_Hf3 zenon_Hec zenon_Hf0 zenon_Hcb zenon_Ha3 zenon_H327 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.65 apply (zenon_L39_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.65 apply (zenon_L802_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.65 apply (zenon_L41_); trivial. % 51.40/51.65 apply (zenon_L24_); trivial. % 51.40/51.65 (* end of lemma zenon_L803_ *) % 51.40/51.65 assert (zenon_L804_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e10)) = (e13)) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.40/51.65 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H2c zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_H35 zenon_H66 zenon_H4b zenon_H327 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.40/51.65 apply (zenon_L39_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.40/51.65 apply (zenon_L794_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.40/51.65 apply (zenon_L41_); trivial. % 51.40/51.65 apply (zenon_L24_); trivial. % 51.40/51.65 (* end of lemma zenon_L804_ *) % 51.40/51.65 assert (zenon_L805_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.40/51.65 do 0 intro. intros zenon_Hcf zenon_H327 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_Hb8 zenon_Hc8 zenon_H131 zenon_Hbe zenon_H321 zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_H1c zenon_Hc2 zenon_Hf3 zenon_Hcb zenon_Hde zenon_H8c zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H35 zenon_H90 zenon_Hab zenon_Hd3 zenon_H2c zenon_H4b zenon_Hb5 zenon_H3d zenon_H19. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.40/51.65 apply (zenon_L804_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.40/51.65 apply (zenon_L42_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.40/51.65 apply (zenon_L417_); trivial. % 51.40/51.65 apply (zenon_L37_); trivial. % 51.40/51.65 (* end of lemma zenon_L805_ *) % 51.40/51.65 assert (zenon_L806_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (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 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H19 zenon_H3d zenon_Hb5 zenon_H4b zenon_Hd3 zenon_Hab zenon_H90 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_H8c zenon_Hde zenon_Hcb zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_H128 zenon_H108 zenon_H321 zenon_H131 zenon_Hc8 zenon_Hb8 zenon_H327 zenon_Hcf zenon_H35 zenon_Hbe zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.40/51.65 apply (zenon_L805_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.40/51.65 apply (zenon_L308_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.40/51.65 apply (zenon_L793_); trivial. % 51.40/51.65 apply (zenon_L46_); trivial. % 51.40/51.65 (* end of lemma zenon_L806_ *) % 51.40/51.65 assert (zenon_L807_ : ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e12) (e12)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_Hbe zenon_H35 zenon_Hcf zenon_H327 zenon_Hb8 zenon_Hc8 zenon_H131 zenon_H321 zenon_H108 zenon_H128 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hcb zenon_Hde zenon_H8c zenon_H54 zenon_He2 zenon_H7d zenon_H42 zenon_H90 zenon_H4b zenon_Hb5 zenon_H3d zenon_H19 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.40/51.65 apply (zenon_L806_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.40/51.65 apply (zenon_L34_); trivial. % 51.40/51.65 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.40/51.65 apply (zenon_L45_); trivial. % 51.40/51.65 apply (zenon_L46_); trivial. % 51.40/51.65 (* end of lemma zenon_L807_ *) % 51.40/51.65 assert (zenon_L808_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (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 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.40/51.65 do 0 intro. intros zenon_H324 zenon_He6 zenon_H2db zenon_H50 zenon_Hda zenon_H2c zenon_Hd3 zenon_Hab zenon_H3d zenon_Hb5 zenon_H4b zenon_H90 zenon_H42 zenon_H7d zenon_He2 zenon_H54 zenon_H8c zenon_Hde zenon_Hcb zenon_Hf3 zenon_Hec zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H128 zenon_H108 zenon_H131 zenon_Hc8 zenon_Hb8 zenon_H327 zenon_Hcf zenon_H35 zenon_Hbe zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H1c zenon_H19 zenon_Hc2. % 51.40/51.65 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.50/51.65 apply (zenon_L56_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.50/51.65 apply (zenon_L303_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.50/51.65 apply (zenon_L807_); trivial. % 51.50/51.65 apply (zenon_L41_); trivial. % 51.50/51.65 (* end of lemma zenon_L808_ *) % 51.50/51.65 assert (zenon_L809_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (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) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> False). % 51.50/51.65 do 0 intro. intros zenon_H324 zenon_H125 zenon_H2db zenon_H50 zenon_H3d zenon_Hb5 zenon_H2c zenon_Hd3 zenon_Hab zenon_H4b zenon_Hde zenon_H7d zenon_H62 zenon_He2 zenon_H54 zenon_Hcb zenon_Hf3 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H49 zenon_Hda zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_H42 zenon_H327 zenon_H35 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_Hcf zenon_H1c zenon_H19 zenon_Hc2. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H324); [ zenon_intro zenon_H22 | zenon_intro zenon_H325 ]. % 51.50/51.65 apply (zenon_L106_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H325); [ zenon_intro zenon_H126 | zenon_intro zenon_H326 ]. % 51.50/51.65 apply (zenon_L303_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H326); [ zenon_intro zenon_H321 | zenon_intro zenon_Hc1 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.50/51.65 apply (zenon_L794_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.50/51.65 apply (zenon_L40_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.50/51.65 apply (zenon_L411_); trivial. % 51.50/51.65 apply (zenon_L37_); trivial. % 51.50/51.65 apply (zenon_L41_); trivial. % 51.50/51.65 (* end of lemma zenon_L809_ *) % 51.50/51.65 assert (zenon_L810_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 51.50/51.65 do 0 intro. intros zenon_Hb0 zenon_Hc2 zenon_Hcf zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_H35 zenon_H327 zenon_H42 zenon_H131 zenon_Hbe zenon_H108 zenon_H128 zenon_Hda zenon_H49 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_He8 zenon_Hec zenon_Hf3 zenon_Hcb zenon_He2 zenon_H62 zenon_H7d zenon_Hde zenon_H4b zenon_Hd3 zenon_Hb5 zenon_H2db zenon_H125 zenon_H324 zenon_H54 zenon_Hab zenon_H1c zenon_H2c zenon_Haf zenon_H8c zenon_H90 zenon_H3d zenon_H19. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_H66 | zenon_intro zenon_Hd0 ]. % 51.50/51.65 apply (zenon_L794_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hd1 ]. % 51.50/51.65 apply (zenon_L40_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hd1); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hb3 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hb5); [ zenon_intro zenon_H4a | zenon_intro zenon_Hb6 ]. % 51.50/51.65 apply (zenon_L335_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hb6); [ zenon_intro zenon_H51 | zenon_intro zenon_Hb7 ]. % 51.50/51.65 apply (zenon_L372_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hb7); [ zenon_intro zenon_H96 | zenon_intro zenon_Hb3 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hb0); [ zenon_intro zenon_H50 | zenon_intro zenon_Hb1 ]. % 51.50/51.65 apply (zenon_L809_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha5 | zenon_intro zenon_Hb2 ]. % 51.50/51.65 apply (zenon_L33_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hb2); [ zenon_intro zenon_Haa | zenon_intro zenon_H51 ]. % 51.50/51.65 apply (zenon_L34_); trivial. % 51.50/51.65 apply (zenon_L35_); trivial. % 51.50/51.65 apply (zenon_L37_); trivial. % 51.50/51.65 apply (zenon_L37_); trivial. % 51.50/51.65 (* end of lemma zenon_L810_ *) % 51.50/51.65 assert (zenon_L811_ : ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op1 (e12) (e10)) = (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) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.50/51.65 do 0 intro. intros zenon_H19 zenon_H3d zenon_H90 zenon_H8c zenon_Haf zenon_H54 zenon_H324 zenon_H125 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hde zenon_H7d zenon_H62 zenon_He2 zenon_Hcb zenon_Hf3 zenon_Hec zenon_He8 zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_H42 zenon_H327 zenon_H35 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_Hcf zenon_Hc2 zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.50/51.65 apply (zenon_L810_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.50/51.65 apply (zenon_L34_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.50/51.65 apply (zenon_L45_); trivial. % 51.50/51.65 apply (zenon_L46_); trivial. % 51.50/51.65 (* end of lemma zenon_L811_ *) % 51.50/51.65 assert (zenon_L812_ : (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e13))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.50/51.65 do 0 intro. intros zenon_Hd3 zenon_Hab zenon_Hb0 zenon_Hcf zenon_H327 zenon_H42 zenon_H131 zenon_Hbe zenon_H108 zenon_H128 zenon_H9e zenon_H12c zenon_He1 zenon_Hf0 zenon_Hec zenon_Hf3 zenon_Hcb zenon_He2 zenon_H62 zenon_H7d zenon_Hde zenon_H4b zenon_Hb5 zenon_H2db zenon_H125 zenon_H324 zenon_H54 zenon_Haf zenon_H90 zenon_H3d zenon_H8c zenon_H19 zenon_Hc2 zenon_H35 zenon_Hb8 zenon_Hc8 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_H1c zenon_Hda. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.50/51.65 apply (zenon_L811_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.50/51.65 apply (zenon_L309_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.50/51.65 apply (zenon_L793_); trivial. % 51.50/51.65 apply (zenon_L46_); trivial. % 51.50/51.65 (* end of lemma zenon_L812_ *) % 51.50/51.65 assert (zenon_L813_ : ((op1 (e10) (e12)) = (e13)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (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) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e13) (e11)) = (e10)) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.50/51.65 do 0 intro. intros zenon_He6 zenon_Hda zenon_H1c zenon_H2c zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hc2 zenon_H3d zenon_H90 zenon_Haf zenon_H54 zenon_H324 zenon_H125 zenon_H2db zenon_Hb5 zenon_H4b zenon_Hde zenon_H7d zenon_He2 zenon_Hcb zenon_Hf3 zenon_Hec zenon_Hf0 zenon_He1 zenon_H12c zenon_H9e zenon_H128 zenon_H108 zenon_Hbe zenon_H131 zenon_H42 zenon_H327 zenon_Hcf zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H19 zenon_H8c. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.50/51.65 apply (zenon_L47_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.50/51.65 apply (zenon_L808_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.50/51.65 apply (zenon_L812_); trivial. % 51.50/51.65 apply (zenon_L24_); trivial. % 51.50/51.65 (* end of lemma zenon_L813_ *) % 51.50/51.65 assert (zenon_L814_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e12) (e10)) = (e11)) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((e10) = (e12))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.50/51.65 do 0 intro. intros zenon_Hfe zenon_H2b zenon_H10b zenon_Hfb zenon_H23 zenon_Hb5 zenon_H10e zenon_H49 zenon_H9e zenon_H54 zenon_H95 zenon_Hab zenon_Hcf zenon_H42 zenon_Hea zenon_He1 zenon_Hb0 zenon_H3d zenon_H10a zenon_Hc8 zenon_Hb8 zenon_Hda zenon_H2c zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_H35 zenon_H4b zenon_H327 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfe); [ zenon_intro zenon_H2d | zenon_intro zenon_H100 ]. % 51.50/51.65 apply (zenon_L7_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H100); [ zenon_intro zenon_H34 | zenon_intro zenon_H101 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.50/51.65 apply (zenon_L317_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.50/51.65 apply (zenon_L86_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.50/51.65 apply (zenon_L421_); trivial. % 51.50/51.65 apply (zenon_L804_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H101); [ zenon_intro zenon_H7c | zenon_intro zenon_He8 ]. % 51.50/51.65 apply (zenon_L75_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.50/51.65 apply (zenon_L317_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.50/51.65 apply (zenon_L354_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.50/51.65 apply (zenon_L421_); trivial. % 51.50/51.65 apply (zenon_L804_); trivial. % 51.50/51.65 (* end of lemma zenon_L814_ *) % 51.50/51.65 assert (zenon_L815_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> ((op1 (e10) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.50/51.65 do 0 intro. intros zenon_Hda zenon_H2c zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_Hc8 zenon_Hb8 zenon_H35 zenon_Hde zenon_H9e zenon_H54 zenon_H95 zenon_Hcf zenon_H4b zenon_H42 zenon_Hea zenon_H41 zenon_He1 zenon_Hb0 zenon_Hab zenon_Hd3 zenon_H311 zenon_H123 zenon_H3b zenon_Hfb zenon_H10e zenon_Hb5 zenon_H30d zenon_H49 zenon_H327 zenon_H7d zenon_H90 zenon_H3d zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.50/51.65 apply (zenon_L39_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.50/51.65 apply (zenon_L799_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.50/51.65 apply (zenon_L41_); trivial. % 51.50/51.65 apply (zenon_L24_); trivial. % 51.50/51.65 (* end of lemma zenon_L815_ *) % 51.50/51.65 assert (zenon_L816_ : (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e12) (e13)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.50/51.65 do 0 intro. intros zenon_H327 zenon_H19 zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H62 zenon_H7d zenon_H49 zenon_H42 zenon_H4b zenon_Hcf zenon_H35 zenon_Hbe zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_H1c zenon_Hda. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H327); [ zenon_intro zenon_He8 | zenon_intro zenon_H328 ]. % 51.50/51.65 apply (zenon_L67_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H328); [ zenon_intro zenon_H2de | zenon_intro zenon_H329 ]. % 51.50/51.65 apply (zenon_L308_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H329); [ zenon_intro zenon_Hf1 | zenon_intro zenon_Hd9 ]. % 51.50/51.65 apply (zenon_L793_); trivial. % 51.50/51.65 apply (zenon_L46_); trivial. % 51.50/51.65 (* end of lemma zenon_L816_ *) % 51.50/51.65 assert (zenon_L817_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((op1 (e13) (e11)) = (e10)) -> (~((e10) = (e12))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.50/51.65 do 0 intro. intros zenon_H90 zenon_Hda zenon_H1c zenon_H2c zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_Hbe zenon_H35 zenon_Hcf zenon_H4b zenon_H42 zenon_H49 zenon_H7d zenon_He2 zenon_H51 zenon_H54 zenon_He1 zenon_H3d zenon_H327 zenon_H19 zenon_H8c. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H90); [ zenon_intro zenon_H4e | zenon_intro zenon_H91 ]. % 51.50/51.65 apply (zenon_L16_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H91); [ zenon_intro zenon_H50 | zenon_intro zenon_H92 ]. % 51.50/51.65 apply (zenon_L17_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H92); [ zenon_intro zenon_H62 | zenon_intro zenon_H8b ]. % 51.50/51.65 apply (zenon_L816_); trivial. % 51.50/51.65 apply (zenon_L24_); trivial. % 51.50/51.65 (* end of lemma zenon_L817_ *) % 51.50/51.65 assert (zenon_L818_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e12))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((e10) = (e11))) -> False). % 51.50/51.65 do 0 intro. intros zenon_Hc8 zenon_Hb8 zenon_H327 zenon_H3d zenon_He1 zenon_H54 zenon_H51 zenon_He2 zenon_H7d zenon_H49 zenon_H42 zenon_H4b zenon_Hcf zenon_H35 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_Hda zenon_H90 zenon_Hc2 zenon_H1c zenon_H19 zenon_H8c. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.50/51.65 apply (zenon_L39_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.50/51.65 apply (zenon_L817_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.50/51.65 apply (zenon_L41_); trivial. % 51.50/51.65 apply (zenon_L24_); trivial. % 51.50/51.65 (* end of lemma zenon_L818_ *) % 51.50/51.65 assert (zenon_L819_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((e10) = (e11))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e22)) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((op1 (e10) (e10)) = (e11)) -> (~((op1 (e12) (e10)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((e10) = (e13))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e13)) = (e12)) -> (~((e12) = (e13))) -> False). % 51.50/51.65 do 0 intro. intros zenon_Hff zenon_H8c zenon_H19 zenon_H1c zenon_Hc2 zenon_H327 zenon_H35 zenon_H40d zenon_H15e zenon_H349 zenon_H2ea zenon_H1d8 zenon_H2c zenon_Hda zenon_Hb8 zenon_Hc8 zenon_Hf8 zenon_H30d zenon_Hb5 zenon_H10e zenon_Hfb zenon_H3b zenon_H123 zenon_H311 zenon_Hd3 zenon_Hab zenon_Hb0 zenon_Hea zenon_H95 zenon_H9e zenon_Hde zenon_H45 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hf3 zenon_He1 zenon_H54 zenon_H7d zenon_H42 zenon_Hcf zenon_H90 zenon_H3d zenon_H11a zenon_H49 zenon_H4b. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.50/51.65 apply (zenon_L11_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.50/51.65 apply (zenon_L11_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.50/51.65 apply (zenon_L815_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.50/51.65 apply (zenon_L815_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.50/51.65 apply (zenon_L13_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.50/51.65 apply (zenon_L803_); trivial. % 51.50/51.65 apply (zenon_L818_); trivial. % 51.50/51.65 apply (zenon_L804_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.50/51.65 apply (zenon_L427_); trivial. % 51.50/51.65 apply (zenon_L15_); trivial. % 51.50/51.65 (* end of lemma zenon_L819_ *) % 51.50/51.65 assert (zenon_L820_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((op2 (e23) (e22)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.50/51.65 do 0 intro. intros zenon_H13b zenon_H30d zenon_H311 zenon_H1d8 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H13b); [ zenon_intro zenon_H23 | zenon_intro zenon_H13e ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H136); [ zenon_intro zenon_H3b | zenon_intro zenon_H139 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.50/51.65 apply (zenon_L11_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.50/51.65 apply (zenon_L801_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.50/51.65 apply (zenon_L801_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.50/51.65 apply (zenon_L299_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.50/51.65 apply (zenon_L803_); trivial. % 51.50/51.65 apply (zenon_L797_); trivial. % 51.50/51.65 apply (zenon_L804_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_H104 | zenon_intro zenon_H13a ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.50/51.65 apply (zenon_L73_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.50/51.65 apply (zenon_L317_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.50/51.65 apply (zenon_L385_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.50/51.65 apply (zenon_L317_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.50/51.65 apply (zenon_L328_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hb9 | zenon_intro zenon_Hc9 ]. % 51.50/51.65 apply (zenon_L39_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hbe | zenon_intro zenon_Hca ]. % 51.50/51.65 apply (zenon_L813_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hc1 | zenon_intro zenon_H8b ]. % 51.50/51.65 apply (zenon_L41_); trivial. % 51.50/51.65 apply (zenon_L24_); trivial. % 51.50/51.65 apply (zenon_L804_); trivial. % 51.50/51.65 apply (zenon_L335_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.50/51.65 apply (zenon_L814_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.50/51.65 apply (zenon_L34_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.50/51.65 apply (zenon_L45_); trivial. % 51.50/51.65 apply (zenon_L46_); trivial. % 51.50/51.65 apply (zenon_L82_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H13a); [ zenon_intro zenon_H11a | zenon_intro zenon_H11c ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H117); [ zenon_intro zenon_H3b | zenon_intro zenon_H118 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_H49 | zenon_intro zenon_Hdf ]. % 51.50/51.65 apply (zenon_L819_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Haa | zenon_intro zenon_He0 ]. % 51.50/51.65 apply (zenon_L34_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_He0); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd9 ]. % 51.50/51.65 apply (zenon_L45_); trivial. % 51.50/51.65 apply (zenon_L46_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_H108 | zenon_intro zenon_H119 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hff); [ zenon_intro zenon_H3c | zenon_intro zenon_H102 ]. % 51.50/51.65 apply (zenon_L317_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H102); [ zenon_intro zenon_H46 | zenon_intro zenon_H103 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfb); [ zenon_intro zenon_H3c | zenon_intro zenon_Hfc ]. % 51.50/51.65 apply (zenon_L317_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfc); [ zenon_intro zenon_H41 | zenon_intro zenon_Hfd ]. % 51.50/51.65 apply (zenon_L328_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_He2 | zenon_intro zenon_H66 ]. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hf8); [ zenon_intro zenon_H41 | zenon_intro zenon_Hf9 ]. % 51.50/51.65 apply (zenon_L328_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hf9); [ zenon_intro zenon_H47 | zenon_intro zenon_Hfa ]. % 51.50/51.65 apply (zenon_L13_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_Hfa); [ zenon_intro zenon_Ha3 | zenon_intro zenon_H51 ]. % 51.50/51.65 apply (zenon_L803_); trivial. % 51.50/51.65 apply (zenon_L797_); trivial. % 51.50/51.65 apply (zenon_L804_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He6 | zenon_intro zenon_H4a ]. % 51.50/51.65 apply (zenon_L427_); trivial. % 51.50/51.65 apply (zenon_L335_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H10a | zenon_intro zenon_H114 ]. % 51.50/51.65 apply (zenon_L512_); trivial. % 51.50/51.65 apply (zenon_L82_); trivial. % 51.50/51.65 apply (zenon_L85_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H1d | zenon_intro zenon_H14b ]. % 51.50/51.65 apply (zenon_L4_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H14b); [ zenon_intro zenon_H22 | zenon_intro zenon_H4e ]. % 51.50/51.65 apply (zenon_L109_); trivial. % 51.50/51.65 apply (zenon_L47_); trivial. % 51.50/51.65 (* end of lemma zenon_L820_ *) % 51.50/51.65 assert (zenon_L821_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e23)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e22))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.50/51.65 do 0 intro. intros zenon_H24e zenon_H14e zenon_H1f7 zenon_H254 zenon_H252 zenon_H22f zenon_H18e zenon_H187 zenon_H19b zenon_H205 zenon_H245 zenon_H244 zenon_H1b1 zenon_H1bd zenon_H1d7 zenon_H175 zenon_H21b zenon_H23c zenon_H209 zenon_H24b zenon_H210 zenon_H1ac zenon_H1fa zenon_H16f zenon_H203 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H15e zenon_H14 zenon_H195. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.50/51.65 apply (zenon_L190_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.50/51.65 apply (zenon_L162_); trivial. % 51.50/51.65 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.50/51.65 apply (zenon_L820_); trivial. % 51.50/51.65 apply (zenon_L126_); trivial. % 51.50/51.65 (* end of lemma zenon_L821_ *) % 51.50/51.65 assert (zenon_L822_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e21)) = (e23)) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H195 zenon_H15e zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H16f zenon_H1fa zenon_H1ac zenon_H24b zenon_H23c zenon_H21b zenon_H175 zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H244 zenon_H245 zenon_H205 zenon_H19b zenon_H187 zenon_H18e zenon_H22f zenon_H252 zenon_H254 zenon_H1f7 zenon_H24e zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.50/51.66 apply (zenon_L151_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.50/51.66 apply (zenon_L821_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.50/51.66 apply (zenon_L153_); trivial. % 51.50/51.66 apply (zenon_L154_); trivial. % 51.50/51.66 (* end of lemma zenon_L822_ *) % 51.50/51.66 assert (zenon_L823_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> ((op2 (e23) (e20)) = (e23)) -> (~((e20) = (e22))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H24e zenon_H1ac zenon_H1cd zenon_H16f zenon_H203 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H15e zenon_H14 zenon_H195. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.50/51.66 apply (zenon_L192_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.50/51.66 apply (zenon_L162_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.50/51.66 apply (zenon_L820_); trivial. % 51.50/51.66 apply (zenon_L126_); trivial. % 51.50/51.66 (* end of lemma zenon_L823_ *) % 51.50/51.66 assert (zenon_L824_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e20) = (e22))) -> ((op2 (e23) (e20)) = (e23)) -> (~((e22) = (e23))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H214 zenon_H1fd zenon_H195 zenon_H15e zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H16f zenon_H1cd zenon_H1ac zenon_H24e zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.50/51.66 apply (zenon_L151_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.50/51.66 apply (zenon_L823_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.50/51.66 apply (zenon_L153_); trivial. % 51.50/51.66 apply (zenon_L154_); trivial. % 51.50/51.66 (* end of lemma zenon_L824_ *) % 51.50/51.66 assert (zenon_L825_ : (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e20) (e22)) = (e23)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H24e zenon_H256 zenon_H2b6 zenon_H21b zenon_H23c zenon_H24b zenon_H210 zenon_H14e zenon_H209 zenon_H16f zenon_H1fd zenon_H214 zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H15e zenon_H14 zenon_H195. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H24e); [ zenon_intro zenon_H21c | zenon_intro zenon_H24f ]. % 51.50/51.66 apply (zenon_L263_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H229 | zenon_intro zenon_H250 ]. % 51.50/51.66 apply (zenon_L163_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H1d8 | zenon_intro zenon_H194 ]. % 51.50/51.66 apply (zenon_L820_); trivial. % 51.50/51.66 apply (zenon_L126_); trivial. % 51.50/51.66 (* end of lemma zenon_L825_ *) % 51.50/51.66 assert (zenon_L826_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e20) (e21)) = (e23))\/(((op2 (e20) (e22)) = (e23))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e20)) = (e22))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((op2 (e20) (e20)) = (e21)) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e22) = (e23))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H28d zenon_H15d zenon_H164 zenon_H168 zenon_H258 zenon_H1fa zenon_H1d7 zenon_H1bd zenon_H1b1 zenon_H245 zenon_H205 zenon_H19b zenon_H187 zenon_H18e zenon_H22f zenon_H254 zenon_H1f7 zenon_H1a7 zenon_H21f zenon_H217 zenon_H1f3 zenon_H1cc zenon_H1e6 zenon_H1ec zenon_H240 zenon_H237 zenon_H259 zenon_H195 zenon_H14 zenon_H15e zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H214 zenon_H1fd zenon_H16f zenon_H209 zenon_H14e zenon_H210 zenon_H24b zenon_H23c zenon_H21b zenon_H2b6 zenon_H24e zenon_H1ac. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.66 apply (zenon_L116_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.66 apply (zenon_L117_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.66 apply (zenon_L118_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.66 apply (zenon_L166_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.66 apply (zenon_L166_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.66 apply (zenon_L182_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.66 apply (zenon_L822_); trivial. % 51.50/51.66 apply (zenon_L824_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.66 apply (zenon_L825_); trivial. % 51.50/51.66 apply (zenon_L132_); trivial. % 51.50/51.66 (* end of lemma zenon_L826_ *) % 51.50/51.66 assert (zenon_L827_ : (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e21)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e20) (e23)) = (e22)) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H230 zenon_H168 zenon_H180 zenon_H17c zenon_H19f zenon_H14 zenon_H176 zenon_H175 zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H15e zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H169 | zenon_intro zenon_H233 ]. % 51.50/51.66 apply (zenon_L118_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H17f | zenon_intro zenon_H234 ]. % 51.50/51.66 apply (zenon_L123_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H19e | zenon_intro zenon_H1d8 ]. % 51.50/51.66 apply (zenon_L128_); trivial. % 51.50/51.66 apply (zenon_L820_); trivial. % 51.50/51.66 (* end of lemma zenon_L827_ *) % 51.50/51.66 assert (zenon_L828_ : (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((e20) = (e21))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e20)) = (e22)) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H22e zenon_H16d zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H175 zenon_H19f zenon_H168 zenon_H230 zenon_H210 zenon_H14e zenon_H209 zenon_H16f zenon_H1fd zenon_H214 zenon_H225 zenon_H176 zenon_H19b zenon_H180 zenon_H18e zenon_H195 zenon_H164 zenon_H22b zenon_H15e zenon_H14 zenon_H187. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H16e | zenon_intro zenon_H231 ]. % 51.50/51.66 apply (zenon_L120_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H17c | zenon_intro zenon_H232 ]. % 51.50/51.66 apply (zenon_L827_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H17f | zenon_intro zenon_H186 ]. % 51.50/51.66 apply (zenon_L164_); trivial. % 51.50/51.66 apply (zenon_L124_); trivial. % 51.50/51.66 (* end of lemma zenon_L828_ *) % 51.50/51.66 assert (zenon_L829_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e21))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H222 zenon_H15e zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H24e zenon_H209 zenon_H1fd zenon_H214 zenon_H283 zenon_H1fa zenon_H1ac zenon_H210 zenon_H254 zenon_H266 zenon_H205 zenon_H16f zenon_H22f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H27f zenon_H280 zenon_H14 zenon_H1a8 zenon_H203 zenon_H27c zenon_H285 zenon_H1f7 zenon_H14e. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.50/51.66 apply (zenon_L823_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.50/51.66 apply (zenon_L155_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.50/51.66 apply (zenon_L248_); trivial. % 51.50/51.66 apply (zenon_L149_); trivial. % 51.50/51.66 (* end of lemma zenon_L829_ *) % 51.50/51.66 assert (zenon_L830_ : (~((e21) = (e23))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H1f7 zenon_H285 zenon_H27c zenon_H1a8 zenon_H280 zenon_H27f zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H22f zenon_H16f zenon_H205 zenon_H266 zenon_H254 zenon_H1ac zenon_H1fa zenon_H283 zenon_H214 zenon_H1fd zenon_H24e zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H15e zenon_H222 zenon_H209 zenon_H14 zenon_H14e zenon_H210. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.50/51.66 apply (zenon_L151_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.50/51.66 apply (zenon_L829_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.50/51.66 apply (zenon_L153_); trivial. % 51.50/51.66 apply (zenon_L154_); trivial. % 51.50/51.66 (* end of lemma zenon_L830_ *) % 51.50/51.66 assert (zenon_L831_ : (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((e21) = (e23))) -> ((op2 (e22) (e20)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.50/51.66 do 0 intro. intros zenon_H18e zenon_H187 zenon_H19b zenon_H14 zenon_H209 zenon_H222 zenon_H15e zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H24e zenon_H1fd zenon_H214 zenon_H283 zenon_H1fa zenon_H1ac zenon_H205 zenon_H16f zenon_H22f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H27f zenon_H280 zenon_H27c zenon_H285 zenon_H1f7 zenon_H266 zenon_H254 zenon_H14e zenon_H210. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.50/51.66 apply (zenon_L183_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.50/51.66 apply (zenon_L830_); trivial. % 51.50/51.66 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.50/51.66 apply (zenon_L198_); trivial. % 51.50/51.66 apply (zenon_L154_); trivial. % 51.50/51.66 (* end of lemma zenon_L831_ *) % 51.50/51.67 assert (zenon_L832_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e23)) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H22f zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H205 zenon_H1bc zenon_H195 zenon_H175 zenon_H21d zenon_H1b1 zenon_H252 zenon_H17f zenon_H267 zenon_H1d7 zenon_H14e zenon_H210. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.50/51.67 apply (zenon_L184_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.50/51.67 apply (zenon_L206_); trivial. % 51.50/51.67 apply (zenon_L154_); trivial. % 51.50/51.67 (* end of lemma zenon_L832_ *) % 51.50/51.67 assert (zenon_L833_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e21) = (e23))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op2 (e21) (e20)) = (e20)) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> ((op2 (e21) (e23)) = (e23)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H273 zenon_H254 zenon_H1f7 zenon_H285 zenon_H27c zenon_H280 zenon_H27f zenon_H1ec zenon_H1ac zenon_H1fa zenon_H283 zenon_H24e zenon_H222 zenon_H26d zenon_H203 zenon_H1bd zenon_H22b zenon_H164 zenon_H180 zenon_H225 zenon_H214 zenon_H1fd zenon_H209 zenon_H230 zenon_H168 zenon_H19f zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H16d zenon_H22e zenon_H22f zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H205 zenon_H1bc zenon_H195 zenon_H175 zenon_H21d zenon_H1b1 zenon_H17f zenon_H267 zenon_H1d7 zenon_H14e zenon_H210. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H273); [ zenon_intro zenon_H266 | zenon_intro zenon_H274 ]. % 51.50/51.67 apply (zenon_L831_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H26e | zenon_intro zenon_H275 ]. % 51.50/51.67 apply (zenon_L205_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H176 | zenon_intro zenon_H252 ]. % 51.50/51.67 apply (zenon_L828_); trivial. % 51.50/51.67 apply (zenon_L832_); trivial. % 51.50/51.67 (* end of lemma zenon_L833_ *) % 51.50/51.67 assert (zenon_L834_ : (~((e20) = (e21))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e22)) = (e23)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H210 zenon_H1b1 zenon_H205 zenon_H19b zenon_H16f zenon_H187 zenon_H18e zenon_H15e zenon_H14 zenon_H22f zenon_H22e zenon_H16d zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H19f zenon_H168 zenon_H230 zenon_H209 zenon_H1fd zenon_H214 zenon_H225 zenon_H180 zenon_H164 zenon_H22b zenon_H1bd zenon_H203 zenon_H26d zenon_H222 zenon_H24e zenon_H283 zenon_H1fa zenon_H1ac zenon_H27f zenon_H280 zenon_H27c zenon_H285 zenon_H254 zenon_H273 zenon_H195 zenon_H175 zenon_H21d zenon_H1ec zenon_H17f zenon_H267 zenon_H1d7 zenon_H1f7 zenon_H14e. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H1fa); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1fb ]. % 51.50/51.67 apply (zenon_L132_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H1fb); [ zenon_intro zenon_H1bc | zenon_intro zenon_H1fc ]. % 51.50/51.67 apply (zenon_L833_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H1fc); [ zenon_intro zenon_H1e7 | zenon_intro zenon_H1f8 ]. % 51.50/51.67 apply (zenon_L202_); trivial. % 51.50/51.67 apply (zenon_L149_); trivial. % 51.50/51.67 (* end of lemma zenon_L834_ *) % 51.50/51.67 assert (zenon_L835_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((op2 (e21) (e20)) = (e20)) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((e20) = (e21))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H1d7 zenon_H267 zenon_H17f zenon_H1ec zenon_H175 zenon_H195 zenon_H273 zenon_H254 zenon_H285 zenon_H27c zenon_H280 zenon_H27f zenon_H1ac zenon_H1fa zenon_H283 zenon_H24e zenon_H222 zenon_H26d zenon_H203 zenon_H1bd zenon_H22b zenon_H164 zenon_H180 zenon_H225 zenon_H214 zenon_H1fd zenon_H209 zenon_H230 zenon_H168 zenon_H19f zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H16d zenon_H22e zenon_H22f zenon_H14 zenon_H15e zenon_H18e zenon_H187 zenon_H16f zenon_H19b zenon_H205 zenon_H1b1 zenon_H210 zenon_H1f7 zenon_H14e. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.50/51.67 apply (zenon_L824_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.50/51.67 apply (zenon_L152_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.50/51.67 apply (zenon_L834_); trivial. % 51.50/51.67 apply (zenon_L149_); trivial. % 51.50/51.67 (* end of lemma zenon_L835_ *) % 51.50/51.67 assert (zenon_L836_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((e20) = (e21))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (~((e20) = (e23))) -> (~((e20) = (e22))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H222 zenon_H24e zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H209 zenon_H1fd zenon_H214 zenon_H285 zenon_H210 zenon_H273 zenon_H254 zenon_H205 zenon_H16f zenon_H22f zenon_H26d zenon_H203 zenon_H19f zenon_H14 zenon_H19e zenon_H15e zenon_H1bd zenon_H1b1 zenon_H19b zenon_H187 zenon_H18e zenon_H27c zenon_H1f3 zenon_H280 zenon_H27f zenon_H195 zenon_H175 zenon_H1ec zenon_H267 zenon_H1d7 zenon_H283 zenon_H1ac zenon_H1fa zenon_H1f7 zenon_H14e. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.50/51.67 apply (zenon_L824_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.50/51.67 apply (zenon_L155_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.50/51.67 apply (zenon_L218_); trivial. % 51.50/51.67 apply (zenon_L149_); trivial. % 51.50/51.67 (* end of lemma zenon_L836_ *) % 51.50/51.67 assert (zenon_L837_ : (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e20) (e22)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e22)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e22)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e22)))) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e22))) -> (~((e20) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e20) = (e21))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> False). % 51.50/51.67 do 0 intro. intros zenon_H22e zenon_H16d zenon_H168 zenon_H230 zenon_H225 zenon_H180 zenon_H164 zenon_H22b zenon_H14e zenon_H1f7 zenon_H1fa zenon_H1ac zenon_H283 zenon_H1d7 zenon_H267 zenon_H1ec zenon_H175 zenon_H195 zenon_H27f zenon_H280 zenon_H1f3 zenon_H27c zenon_H18e zenon_H187 zenon_H19b zenon_H1b1 zenon_H1bd zenon_H15e zenon_H14 zenon_H19f zenon_H203 zenon_H26d zenon_H22f zenon_H16f zenon_H205 zenon_H254 zenon_H273 zenon_H210 zenon_H285 zenon_H214 zenon_H1fd zenon_H209 zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H24e zenon_H222 zenon_H21b zenon_H21c. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H169 | zenon_intro zenon_H233 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H17f | zenon_intro zenon_H234 ]. % 51.50/51.67 apply (zenon_L835_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H19e | zenon_intro zenon_H1d8 ]. % 51.50/51.67 apply (zenon_L836_); trivial. % 51.50/51.67 apply (zenon_L157_); trivial. % 51.50/51.67 (* end of lemma zenon_L837_ *) % 51.50/51.67 assert (zenon_L838_ : (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((e11) = (e12))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((e11) = (e13))) -> (~((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 (e12) (e10)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((e20) = (e23))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e22) (e23)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e22) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H222 zenon_H210 zenon_H209 zenon_H24e zenon_H16f zenon_Hda zenon_H1c zenon_H2c zenon_Hd3 zenon_Hab zenon_H35 zenon_Hde zenon_H135 zenon_H24 zenon_Hb0 zenon_Hf6 zenon_H54 zenon_H10e zenon_H7d zenon_H72 zenon_Haf zenon_H8c zenon_H117 zenon_H105 zenon_Hfe zenon_H2b zenon_H10b zenon_H90 zenon_Hcb zenon_Hf0 zenon_Hec zenon_Hc2 zenon_Hf3 zenon_Hb5 zenon_H4b zenon_H42 zenon_H9e zenon_H12c zenon_He1 zenon_H3d zenon_H128 zenon_H125 zenon_H131 zenon_H123 zenon_H113 zenon_Hff zenon_Hf8 zenon_H45 zenon_H95 zenon_H65 zenon_Ha2 zenon_Hfb zenon_Hcf zenon_Hea zenon_Hc8 zenon_H136 zenon_Hb8 zenon_H19 zenon_H1b zenon_H2d4 zenon_H2db zenon_H324 zenon_H2e1 zenon_H2ba zenon_H2c5 zenon_H2c9 zenon_H327 zenon_H40d zenon_H349 zenon_H2ea zenon_H311 zenon_H30d zenon_H13b zenon_H1fd zenon_H214 zenon_H205 zenon_H1f3 zenon_H1c9 zenon_H28c zenon_H187 zenon_H14 zenon_H15e zenon_H1e6 zenon_H1bd zenon_H203 zenon_H26e zenon_H26d zenon_H175 zenon_H195 zenon_H1d7 zenon_H1ac zenon_H1fa zenon_H1f7 zenon_H14e. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H1cd | zenon_intro zenon_H223 ]. % 51.50/51.67 apply (zenon_L824_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H223); [ zenon_intro zenon_H204 | zenon_intro zenon_H224 ]. % 51.50/51.67 apply (zenon_L152_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H21d | zenon_intro zenon_H1f8 ]. % 51.50/51.67 apply (zenon_L228_); trivial. % 51.50/51.67 apply (zenon_L149_); trivial. % 51.50/51.67 (* end of lemma zenon_L838_ *) % 51.50/51.67 assert (zenon_L839_ : (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e22) (e20)) = (e21)) -> ((op2 (e23) (e21)) = (e20)) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e12) (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)))) -> (~((e11) = (e13))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e11) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (op1 (e13) (e13))) (e13))) -> ((e10) = (op1 (e13) (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((e20) = (e22))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e23))\/(((op2 (e23) (e21)) = (e23))\/(((op2 (e23) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> (~((e20) = (e21))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H22f zenon_H16d zenon_H1a7 zenon_H1f7 zenon_H1fa zenon_H1ac zenon_H1d7 zenon_H195 zenon_H175 zenon_H26d zenon_H26e zenon_H203 zenon_H1bd zenon_H1e6 zenon_H15e zenon_H14 zenon_H187 zenon_H28c zenon_H1f3 zenon_H205 zenon_H214 zenon_H1fd zenon_H13b zenon_H30d zenon_H311 zenon_H2ea zenon_H349 zenon_H40d zenon_H327 zenon_H2c9 zenon_H2c5 zenon_H2ba zenon_H2e1 zenon_H324 zenon_H2db zenon_H2d4 zenon_H1b zenon_H19 zenon_Hb8 zenon_H136 zenon_Hc8 zenon_Hea zenon_Hcf zenon_Hfb zenon_Ha2 zenon_H65 zenon_H95 zenon_H45 zenon_Hf8 zenon_Hff zenon_H113 zenon_H123 zenon_H131 zenon_H125 zenon_H128 zenon_H3d zenon_He1 zenon_H12c zenon_H9e zenon_H42 zenon_H4b zenon_Hb5 zenon_Hf3 zenon_Hc2 zenon_Hec zenon_Hf0 zenon_Hcb zenon_H90 zenon_H10b zenon_H2b zenon_Hfe zenon_H105 zenon_H117 zenon_H8c zenon_Haf zenon_H72 zenon_H7d zenon_H10e zenon_H54 zenon_Hf6 zenon_Hb0 zenon_H24 zenon_H135 zenon_Hde zenon_H35 zenon_Hab zenon_Hd3 zenon_H2c zenon_H1c zenon_Hda zenon_H16f zenon_H24e zenon_H209 zenon_H222 zenon_H14e zenon_H210. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1a5 | zenon_intro zenon_H235 ]. % 51.50/51.67 apply (zenon_L129_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H236 ]. % 51.50/51.67 apply (zenon_L130_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H1c9 | zenon_intro zenon_H20f ]. % 51.50/51.67 apply (zenon_L838_); trivial. % 51.50/51.67 apply (zenon_L154_); trivial. % 51.50/51.67 (* end of lemma zenon_L839_ *) % 51.50/51.67 assert (zenon_L840_ : (~((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e11) = (op1 (e13) (e13))) -> ((h4 (e13)) = (e23)) -> False). % 51.50/51.67 do 0 intro. intros zenon_H413 zenon_H2e7 zenon_H19 zenon_H2ea. % 51.50/51.67 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))). % 51.50/51.67 intro zenon_D_pnotp. % 51.50/51.67 apply zenon_H413. % 51.50/51.67 rewrite <- zenon_D_pnotp. % 51.50/51.67 exact zenon_H2e7. % 51.50/51.67 cut (((op2 (e23) (e23)) = (op2 (h4 (e13)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H414]. % 51.50/51.67 cut (((h4 (e11)) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H415]. % 51.50/51.67 congruence. % 51.50/51.67 elim (classic ((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [ zenon_intro zenon_H416 | zenon_intro zenon_H417 ]. % 51.50/51.67 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13)))) = ((h4 (e11)) = (h4 (op1 (e13) (e13))))). % 51.50/51.67 intro zenon_D_pnotp. % 51.50/51.67 apply zenon_H415. % 51.50/51.67 rewrite <- zenon_D_pnotp. % 51.50/51.67 exact zenon_H416. % 51.50/51.67 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H417]. % 51.50/51.67 cut (((h4 (op1 (e13) (e13))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H418]. % 51.50/51.67 congruence. % 51.50/51.67 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 51.50/51.67 congruence. % 51.50/51.67 apply zenon_H1a. apply sym_equal. exact zenon_H19. % 51.50/51.67 apply zenon_H417. apply refl_equal. % 51.50/51.67 apply zenon_H417. apply refl_equal. % 51.50/51.67 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H35d]. % 51.50/51.67 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H35d]. % 51.50/51.67 congruence. % 51.50/51.67 apply zenon_H35d. apply sym_equal. exact zenon_H2ea. % 51.50/51.67 apply zenon_H35d. apply sym_equal. exact zenon_H2ea. % 51.50/51.67 (* end of lemma zenon_L840_ *) % 51.50/51.67 assert (zenon_L841_ : (~(((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))) -> ((h4 (e10)) = (op2 (e23) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (op2 (e23) (e23)))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H419 zenon_H13 zenon_H14. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H419). zenon_intro zenon_H12. zenon_intro zenon_H41a. % 51.50/51.67 apply (zenon_L1_); trivial. % 51.50/51.67 (* end of lemma zenon_L841_ *) % 51.50/51.67 assert (zenon_L842_ : (~(((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H41b zenon_H2e7 zenon_H14e. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H41b). zenon_intro zenon_H41d. zenon_intro zenon_H41c. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H41c). zenon_intro zenon_H2e6. zenon_intro zenon_H41e. % 51.50/51.67 apply (zenon_L326_); trivial. % 51.50/51.67 (* end of lemma zenon_L842_ *) % 51.50/51.67 assert (zenon_L843_ : (~(((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))) -> ((h4 (e12)) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (e23) (op2 (e23) (e23))) (e23))) -> False). % 51.50/51.67 do 0 intro. intros zenon_H41f zenon_H349 zenon_H15e. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H41f). zenon_intro zenon_H421. zenon_intro zenon_H420. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H420). zenon_intro zenon_H423. zenon_intro zenon_H422. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H422). zenon_intro zenon_H348. zenon_intro zenon_H424. % 51.50/51.67 apply (zenon_L487_); trivial. % 51.50/51.67 (* end of lemma zenon_L843_ *) % 51.50/51.67 assert (zenon_L844_ : (~(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23)))))) -> ((h4 (e13)) = (e23)) -> False). % 51.50/51.67 do 0 intro. intros zenon_H425 zenon_H2ea. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H425). zenon_intro zenon_H427. zenon_intro zenon_H426. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H426). zenon_intro zenon_H429. zenon_intro zenon_H428. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H428). zenon_intro zenon_H42a. zenon_intro zenon_H399. % 51.50/51.67 exact (zenon_H399 zenon_H2ea). % 51.50/51.67 (* end of lemma zenon_L844_ *) % 51.50/51.67 apply NNPP. intro zenon_G. % 51.50/51.67 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H42c. zenon_intro zenon_H42b. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H42b). zenon_intro zenon_H2d4. zenon_intro zenon_H42d. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H42d). zenon_intro zenon_H2d1. zenon_intro zenon_H42e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H42e). zenon_intro zenon_H430. zenon_intro zenon_H42f. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H42f). zenon_intro zenon_H432. zenon_intro zenon_H431. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H431). zenon_intro zenon_H434. zenon_intro zenon_H433. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H433). zenon_intro zenon_H131. zenon_intro zenon_H435. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H435). zenon_intro zenon_Hb0. zenon_intro zenon_H436. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H436). zenon_intro zenon_H311. zenon_intro zenon_H437. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H437). zenon_intro zenon_H439. zenon_intro zenon_H438. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H438). zenon_intro zenon_H3dc. zenon_intro zenon_H43a. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H43a). zenon_intro zenon_H43c. zenon_intro zenon_H43b. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H43b). zenon_intro zenon_H31b. zenon_intro zenon_H43d. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H43d). zenon_intro zenon_H43f. zenon_intro zenon_H43e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H43e). zenon_intro zenon_Hf3. zenon_intro zenon_H440. % 51.50/51.67 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H13b. zenon_intro zenon_H441. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H441). zenon_intro zenon_H135. zenon_intro zenon_H442. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H442). zenon_intro zenon_H136. zenon_intro zenon_H443. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H443). zenon_intro zenon_H117. zenon_intro zenon_H444. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H444). zenon_intro zenon_H32a. zenon_intro zenon_H445. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H445). zenon_intro zenon_Hfe. zenon_intro zenon_H446. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H446). zenon_intro zenon_Hff. zenon_intro zenon_H447. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H447). zenon_intro zenon_Hfb. zenon_intro zenon_H448. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H448). zenon_intro zenon_H2e0. zenon_intro zenon_H449. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H449). zenon_intro zenon_H44b. zenon_intro zenon_H44a. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H44a). zenon_intro zenon_H318. zenon_intro zenon_H44c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H44c). zenon_intro zenon_H3b9. zenon_intro zenon_H44d. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H44d). zenon_intro zenon_H341. zenon_intro zenon_H44e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H44e). zenon_intro zenon_H2e1. zenon_intro zenon_H44f. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H44f). zenon_intro zenon_Hf8. zenon_intro zenon_H450. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H450). zenon_intro zenon_H452. zenon_intro zenon_H451. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H451). zenon_intro zenon_H454. zenon_intro zenon_H453. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H453). zenon_intro zenon_H324. zenon_intro zenon_H455. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H455). zenon_intro zenon_H33e. zenon_intro zenon_H456. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H456). zenon_intro zenon_H345. zenon_intro zenon_H457. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H457). zenon_intro zenon_H314. zenon_intro zenon_H458. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H458). zenon_intro zenon_H31e. zenon_intro zenon_H459. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H459). zenon_intro zenon_H45b. zenon_intro zenon_H45a. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H45a). zenon_intro zenon_H3d9. zenon_intro zenon_H45c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H45c). zenon_intro zenon_Hc8. zenon_intro zenon_H45d. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H45d). zenon_intro zenon_H90. zenon_intro zenon_H45e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H45e). zenon_intro zenon_H460. zenon_intro zenon_H45f. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H45f). zenon_intro zenon_H462. zenon_intro zenon_H461. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H461). zenon_intro zenon_H327. zenon_intro zenon_H463. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H463). zenon_intro zenon_Hde. zenon_intro zenon_H464. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H464). zenon_intro zenon_Hcf. zenon_intro zenon_Hb5. % 51.50/51.67 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H466. zenon_intro zenon_H465. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H465). zenon_intro zenon_H468. zenon_intro zenon_H467. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H467). zenon_intro zenon_H3c2. zenon_intro zenon_H469. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H469). zenon_intro zenon_H46b. zenon_intro zenon_H46a. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H46a). zenon_intro zenon_H46d. zenon_intro zenon_H46c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H46c). zenon_intro zenon_H46f. zenon_intro zenon_H46e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H46e). zenon_intro zenon_H285. zenon_intro zenon_H470. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H470). zenon_intro zenon_H1f3. zenon_intro zenon_H471. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H471). zenon_intro zenon_H273. zenon_intro zenon_H472. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H472). zenon_intro zenon_H474. zenon_intro zenon_H473. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H473). zenon_intro zenon_H476. zenon_intro zenon_H475. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H475). zenon_intro zenon_H29d. zenon_intro zenon_H477. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H477). zenon_intro zenon_H21f. zenon_intro zenon_H478. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H478). zenon_intro zenon_H47a. zenon_intro zenon_H479. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H479). zenon_intro zenon_H24b. zenon_intro zenon_H47b. % 51.50/51.67 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H47d. zenon_intro zenon_H47c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H47c). zenon_intro zenon_H2ae. zenon_intro zenon_H47e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H47e). zenon_intro zenon_H2a5. zenon_intro zenon_H47f. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H47f). zenon_intro zenon_H2a7. zenon_intro zenon_H480. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H480). zenon_intro zenon_H28d. zenon_intro zenon_H481. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H481). zenon_intro zenon_H28e. zenon_intro zenon_H482. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H482). zenon_intro zenon_H258. zenon_intro zenon_H483. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H483). zenon_intro zenon_H259. zenon_intro zenon_H484. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H484). zenon_intro zenon_H2a6. zenon_intro zenon_H485. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H485). zenon_intro zenon_H487. zenon_intro zenon_H486. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H486). zenon_intro zenon_H489. zenon_intro zenon_H488. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H488). zenon_intro zenon_H48b. zenon_intro zenon_H48a. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H48a). zenon_intro zenon_H22e. zenon_intro zenon_H48c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H48c). zenon_intro zenon_H22b. zenon_intro zenon_H48d. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H48d). zenon_intro zenon_H48f. zenon_intro zenon_H48e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H48e). zenon_intro zenon_H491. zenon_intro zenon_H490. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H490). zenon_intro zenon_H493. zenon_intro zenon_H492. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H492). zenon_intro zenon_H495. zenon_intro zenon_H494. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H494). zenon_intro zenon_H3c5. zenon_intro zenon_H496. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H496). zenon_intro zenon_H498. zenon_intro zenon_H497. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H497). zenon_intro zenon_H2af. zenon_intro zenon_H499. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H499). zenon_intro zenon_H230. zenon_intro zenon_H49a. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H49a). zenon_intro zenon_H3df. zenon_intro zenon_H49b. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H49b). zenon_intro zenon_H3e2. zenon_intro zenon_H49c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H49c). zenon_intro zenon_H214. zenon_intro zenon_H49d. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H49d). zenon_intro zenon_H22f. zenon_intro zenon_H49e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H49e). zenon_intro zenon_H4a0. zenon_intro zenon_H49f. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H49f). zenon_intro zenon_H4a2. zenon_intro zenon_H4a1. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4a1). zenon_intro zenon_H24e. zenon_intro zenon_H4a3. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4a3). zenon_intro zenon_H19b. zenon_intro zenon_H4a4. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4a4). zenon_intro zenon_H222. zenon_intro zenon_H1fa. % 51.50/51.67 apply (zenon_and_s _ _ ax5). zenon_intro zenon_Hea. zenon_intro zenon_H4a5. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4a5). zenon_intro zenon_H7d. zenon_intro zenon_H4a6. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4a6). zenon_intro zenon_H65. zenon_intro zenon_H4a7. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4a7). zenon_intro zenon_H4a9. zenon_intro zenon_H4a8. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4a8). zenon_intro zenon_H4ab. zenon_intro zenon_H4aa. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4aa). zenon_intro zenon_H30d. zenon_intro zenon_H4ac. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ac). zenon_intro zenon_H45. zenon_intro zenon_H4ad. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ad). zenon_intro zenon_H4af. zenon_intro zenon_H4ae. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ae). zenon_intro zenon_H1b. zenon_intro zenon_H4b0. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b0). zenon_intro zenon_H2c9. zenon_intro zenon_H4b1. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b1). zenon_intro zenon_H10e. zenon_intro zenon_H4b2. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b2). zenon_intro zenon_H4b4. zenon_intro zenon_H4b3. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b3). zenon_intro zenon_H125. zenon_intro zenon_H4b5. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b5). zenon_intro zenon_H2ce. zenon_intro zenon_H4b6. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b6). zenon_intro zenon_H33a. zenon_intro zenon_H4b7. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b7). zenon_intro zenon_H12c. zenon_intro zenon_H4b8. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b8). zenon_intro zenon_Hcb. zenon_intro zenon_H4b9. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4b9). zenon_intro zenon_He1. zenon_intro zenon_H4ba. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ba). zenon_intro zenon_Hab. zenon_intro zenon_H4bb. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4bb). zenon_intro zenon_Hd3. zenon_intro zenon_H4bc. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4bc). zenon_intro zenon_Hda. zenon_intro zenon_H4bd. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4bd). zenon_intro zenon_Haf. zenon_intro zenon_H4be. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4be). zenon_intro zenon_H54. zenon_intro zenon_H4bf. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4bf). zenon_intro zenon_H9e. zenon_intro zenon_H4c0. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c0). zenon_intro zenon_H105. zenon_intro zenon_H4c1. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c1). zenon_intro zenon_H24. zenon_intro zenon_H4c2. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c2). zenon_intro zenon_H2b. zenon_intro zenon_H4c3. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c3). zenon_intro zenon_H4c5. zenon_intro zenon_H4c4. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c4). zenon_intro zenon_H2ba. zenon_intro zenon_H4c6. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c6). zenon_intro zenon_H2be. zenon_intro zenon_H4c7. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c7). zenon_intro zenon_H2c5. zenon_intro zenon_H4c8. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c8). zenon_intro zenon_H128. zenon_intro zenon_H4c9. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4c9). zenon_intro zenon_Hf6. zenon_intro zenon_H4ca. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ca). zenon_intro zenon_Ha2. zenon_intro zenon_H4cb. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4cb). zenon_intro zenon_H72. zenon_intro zenon_H4cc. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4cc). zenon_intro zenon_H2db. zenon_intro zenon_H4cd. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4cd). zenon_intro zenon_H2ff. zenon_intro zenon_H4ce. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ce). zenon_intro zenon_H305. zenon_intro zenon_H4cf. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4cf). zenon_intro zenon_H123. zenon_intro zenon_H4d0. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d0). zenon_intro zenon_H4d2. zenon_intro zenon_H4d1. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d1). zenon_intro zenon_H4d4. zenon_intro zenon_H4d3. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d3). zenon_intro zenon_H95. zenon_intro zenon_H4d5. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d5). zenon_intro zenon_Hb8. zenon_intro zenon_H4d6. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d6). zenon_intro zenon_Hf0. zenon_intro zenon_H4d7. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d7). zenon_intro zenon_H113. zenon_intro zenon_H4d8. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d8). zenon_intro zenon_Hc2. zenon_intro zenon_H4d9. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4d9). zenon_intro zenon_H3b3. zenon_intro zenon_Hec. % 51.50/51.67 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H240. zenon_intro zenon_H4da. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4da). zenon_intro zenon_H1b1. zenon_intro zenon_H4db. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4db). zenon_intro zenon_H1cc. zenon_intro zenon_H4dc. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4dc). zenon_intro zenon_H4de. zenon_intro zenon_H4dd. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4dd). zenon_intro zenon_H4e0. zenon_intro zenon_H4df. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4df). zenon_intro zenon_H262. zenon_intro zenon_H4e1. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e1). zenon_intro zenon_H245. zenon_intro zenon_H4e2. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e2). zenon_intro zenon_H3c8. zenon_intro zenon_H4e3. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e3). zenon_intro zenon_H150. zenon_intro zenon_H4e4. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e4). zenon_intro zenon_H36d. zenon_intro zenon_H4e5. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e5). zenon_intro zenon_H26d. zenon_intro zenon_H4e6. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e6). zenon_intro zenon_H4e8. zenon_intro zenon_H4e7. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e7). zenon_intro zenon_H4ea. zenon_intro zenon_H4e9. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4e9). zenon_intro zenon_H2b7. zenon_intro zenon_H4eb. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4eb). zenon_intro zenon_H2b6. zenon_intro zenon_H4ec. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ec). zenon_intro zenon_H267. zenon_intro zenon_H4ed. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ed). zenon_intro zenon_H283. zenon_intro zenon_H4ee. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ee). zenon_intro zenon_H1d7. zenon_intro zenon_H4ef. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ef). zenon_intro zenon_H187. zenon_intro zenon_H4f0. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f0). zenon_intro zenon_H18e. zenon_intro zenon_H4f1. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f1). zenon_intro zenon_H195. zenon_intro zenon_H4f2. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f2). zenon_intro zenon_H28c. zenon_intro zenon_H4f3. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f3). zenon_intro zenon_H1bd. zenon_intro zenon_H4f4. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f4). zenon_intro zenon_H1ec. zenon_intro zenon_H4f5. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f5). zenon_intro zenon_H25f. zenon_intro zenon_H4f6. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f6). zenon_intro zenon_H157. zenon_intro zenon_H4f7. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f7). zenon_intro zenon_H15d. zenon_intro zenon_H4f8. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f8). zenon_intro zenon_H4fa. zenon_intro zenon_H4f9. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4f9). zenon_intro zenon_H164. zenon_intro zenon_H4fb. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4fb). zenon_intro zenon_H168. zenon_intro zenon_H4fc. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4fc). zenon_intro zenon_H36a. zenon_intro zenon_H4fd. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4fd). zenon_intro zenon_H27f. zenon_intro zenon_H4fe. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4fe). zenon_intro zenon_H1a7. zenon_intro zenon_H4ff. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H4ff). zenon_intro zenon_H180. zenon_intro zenon_H500. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H500). zenon_intro zenon_H502. zenon_intro zenon_H501. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H501). zenon_intro zenon_H27c. zenon_intro zenon_H503. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H503). zenon_intro zenon_H225. zenon_intro zenon_H504. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H504). zenon_intro zenon_H19f. zenon_intro zenon_H505. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H505). zenon_intro zenon_H254. zenon_intro zenon_H506. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H506). zenon_intro zenon_H508. zenon_intro zenon_H507. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H507). zenon_intro zenon_H50a. zenon_intro zenon_H509. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H509). zenon_intro zenon_H1e6. zenon_intro zenon_H50b. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H50b). zenon_intro zenon_H1fd. zenon_intro zenon_H50c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H50c). zenon_intro zenon_H21b. zenon_intro zenon_H50d. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H50d). zenon_intro zenon_H217. zenon_intro zenon_H50e. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H50e). zenon_intro zenon_H209. zenon_intro zenon_H50f. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H50f). zenon_intro zenon_H510. zenon_intro zenon_H23c. % 51.50/51.67 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H8c. zenon_intro zenon_H511. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H511). zenon_intro zenon_H35. zenon_intro zenon_H512. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H512). zenon_intro zenon_H42. zenon_intro zenon_H513. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H513). zenon_intro zenon_H10b. zenon_intro zenon_H514. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H514). zenon_intro zenon_H3d. zenon_intro zenon_H4b. % 51.50/51.67 apply (zenon_and_s _ _ ax8). zenon_intro zenon_H210. zenon_intro zenon_H515. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H515). zenon_intro zenon_H16f. zenon_intro zenon_H516. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H516). zenon_intro zenon_H205. zenon_intro zenon_H517. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H517). zenon_intro zenon_H288. zenon_intro zenon_H518. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H518). zenon_intro zenon_H1f7. zenon_intro zenon_H1ac. % 51.50/51.67 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H1c. zenon_intro zenon_H519. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H519). zenon_intro zenon_H19. zenon_intro zenon_H2c. % 51.50/51.67 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H14. zenon_intro zenon_H51a. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H51a). zenon_intro zenon_H14e. zenon_intro zenon_H15e. % 51.50/51.67 apply (zenon_and_s _ _ ax17). zenon_intro zenon_H2ea. zenon_intro zenon_H51b. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H51b). zenon_intro zenon_H13. zenon_intro zenon_H51c. % 51.50/51.67 apply (zenon_and_s _ _ zenon_H51c). zenon_intro zenon_H2e7. zenon_intro zenon_H349. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H51e. zenon_intro zenon_H51d. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H51d). zenon_intro zenon_H520. zenon_intro zenon_H51f. % 51.50/51.67 apply (zenon_notor_s _ _ zenon_H51f). zenon_intro zenon_H522. zenon_intro zenon_H521. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H521); [ zenon_intro zenon_H13d | zenon_intro zenon_H523 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_L110_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H523); [ zenon_intro zenon_H2e9 | zenon_intro zenon_H526 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_L428_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L429_); trivial. % 51.50/51.67 apply (zenon_L132_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H526); [ zenon_intro zenon_H34c | zenon_intro zenon_H527 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_L498_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H527); [ zenon_intro zenon_H357 | zenon_intro zenon_H528 ]. % 51.50/51.67 apply (zenon_L499_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H528); [ zenon_intro zenon_H35f | zenon_intro zenon_H529 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.50/51.67 apply (zenon_L513_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.50/51.67 apply (zenon_L535_); trivial. % 51.50/51.67 apply (zenon_L156_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H529); [ zenon_intro zenon_H375 | zenon_intro zenon_H52a ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L533_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.67 apply (zenon_L182_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.67 apply (zenon_L536_); trivial. % 51.50/51.67 apply (zenon_L547_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L279_); trivial. % 51.50/51.67 apply (zenon_L194_); trivial. % 51.50/51.67 apply (zenon_L534_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H52a); [ zenon_intro zenon_H382 | zenon_intro zenon_H52b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L533_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.67 apply (zenon_L182_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.67 apply (zenon_L536_); trivial. % 51.50/51.67 apply (zenon_L559_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L429_); trivial. % 51.50/51.67 apply (zenon_L132_); trivial. % 51.50/51.67 apply (zenon_L534_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H52b); [ zenon_intro zenon_H38e | zenon_intro zenon_H52c ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L533_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.67 apply (zenon_L182_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.67 apply (zenon_L536_); trivial. % 51.50/51.67 apply (zenon_L575_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L279_); trivial. % 51.50/51.67 apply (zenon_L194_); trivial. % 51.50/51.67 apply (zenon_L534_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H52c); [ zenon_intro zenon_H39a | zenon_intro zenon_H52d ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L533_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_L578_); trivial. % 51.50/51.67 apply (zenon_L534_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H52d); [ zenon_intro zenon_H3ad | zenon_intro zenon_H52e ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L533_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.67 apply (zenon_L182_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.67 apply (zenon_L536_); trivial. % 51.50/51.67 apply (zenon_L623_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L429_); trivial. % 51.50/51.67 apply (zenon_L132_); trivial. % 51.50/51.67 apply (zenon_L534_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_L258_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H52e); [ zenon_intro zenon_H3d2 | zenon_intro zenon_H52f ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L533_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.67 apply (zenon_L182_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.67 apply (zenon_L536_); trivial. % 51.50/51.67 apply (zenon_L704_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L429_); trivial. % 51.50/51.67 apply (zenon_L132_); trivial. % 51.50/51.67 apply (zenon_L534_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H13c | zenon_intro zenon_H2b0 ]. % 51.50/51.67 apply (zenon_L114_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H16d | zenon_intro zenon_H2b1 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L120_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_L707_); trivial. % 51.50/51.67 apply (zenon_L195_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.50/51.67 apply (zenon_L196_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L120_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_L707_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H169 | zenon_intro zenon_H233 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H17f | zenon_intro zenon_H234 ]. % 51.50/51.67 apply (zenon_L722_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H234); [ zenon_intro zenon_H19e | zenon_intro zenon_H1d8 ]. % 51.50/51.67 apply (zenon_L723_); trivial. % 51.50/51.67 apply (zenon_L157_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.50/51.67 apply (zenon_L232_); trivial. % 51.50/51.67 apply (zenon_L156_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_L233_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H266 | zenon_intro zenon_H1fe ]. % 51.50/51.67 apply (zenon_L257_); trivial. % 51.50/51.67 apply (zenon_L151_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H52f); [ zenon_intro zenon_H3ec | zenon_intro zenon_H530 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L259_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.67 apply (zenon_L182_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.67 apply (zenon_L751_); trivial. % 51.50/51.67 apply (zenon_L752_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L429_); trivial. % 51.50/51.67 apply (zenon_L194_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H13c | zenon_intro zenon_H2b0 ]. % 51.50/51.67 apply (zenon_L114_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H16d | zenon_intro zenon_H2b1 ]. % 51.50/51.67 apply (zenon_L754_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H266 | zenon_intro zenon_H1fe ]. % 51.50/51.67 apply (zenon_L257_); trivial. % 51.50/51.67 apply (zenon_L151_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H530); [ zenon_intro zenon_H3f8 | zenon_intro zenon_H531 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_L781_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H13c | zenon_intro zenon_H2b0 ]. % 51.50/51.67 apply (zenon_L114_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H16d | zenon_intro zenon_H2b1 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L782_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.50/51.67 apply (zenon_L196_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L120_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_L780_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.50/51.67 apply (zenon_L151_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.50/51.67 apply (zenon_L789_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.50/51.67 apply (zenon_L153_); trivial. % 51.50/51.67 apply (zenon_L154_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L120_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_L780_); trivial. % 51.50/51.67 apply (zenon_L231_); trivial. % 51.50/51.67 apply (zenon_L156_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_L233_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H266 | zenon_intro zenon_H1fe ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.50/51.67 apply (zenon_L245_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_L784_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.50/51.67 apply (zenon_L256_); trivial. % 51.50/51.67 apply (zenon_L156_); trivial. % 51.50/51.67 apply (zenon_L151_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H531); [ zenon_intro zenon_H3fe | zenon_intro zenon_H532 ]. % 51.50/51.67 apply (zenon_L791_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H532); [ zenon_intro zenon_H40d | zenon_intro zenon_H533 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H47d); [ zenon_intro zenon_H13c | zenon_intro zenon_H524 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L826_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_L280_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H258); [ zenon_intro zenon_H238 | zenon_intro zenon_H25a ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25a); [ zenon_intro zenon_H244 | zenon_intro zenon_H25b ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H259); [ zenon_intro zenon_H238 | zenon_intro zenon_H25c ]. % 51.50/51.67 apply (zenon_L260_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25c); [ zenon_intro zenon_H23b | zenon_intro zenon_H25d ]. % 51.50/51.67 apply (zenon_L182_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25d); [ zenon_intro zenon_H252 | zenon_intro zenon_H1cd ]. % 51.50/51.67 apply (zenon_L822_); trivial. % 51.50/51.67 apply (zenon_L824_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H25b); [ zenon_intro zenon_H256 | zenon_intro zenon_H1ab ]. % 51.50/51.67 apply (zenon_L429_); trivial. % 51.50/51.67 apply (zenon_L132_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H524); [ zenon_intro zenon_H151 | zenon_intro zenon_H525 ]. % 51.50/51.67 apply (zenon_L113_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H525); [ zenon_intro zenon_H156 | zenon_intro zenon_H1a5 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ae); [ zenon_intro zenon_H13c | zenon_intro zenon_H2b0 ]. % 51.50/51.67 apply (zenon_L114_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b0); [ zenon_intro zenon_H16d | zenon_intro zenon_H2b1 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L826_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.50/51.67 apply (zenon_L196_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28e); [ zenon_intro zenon_H15f | zenon_intro zenon_H291 ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H291); [ zenon_intro zenon_H16e | zenon_intro zenon_H292 ]. % 51.50/51.67 apply (zenon_L120_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H292); [ zenon_intro zenon_H176 | zenon_intro zenon_H21c ]. % 51.50/51.67 apply (zenon_L828_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.50/51.67 apply (zenon_L151_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.50/51.67 apply (zenon_L837_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.50/51.67 apply (zenon_L153_); trivial. % 51.50/51.67 apply (zenon_L154_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1fe | zenon_intro zenon_H215 ]. % 51.50/51.67 apply (zenon_L151_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H203 | zenon_intro zenon_H216 ]. % 51.50/51.67 apply (zenon_L839_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H208 | zenon_intro zenon_H20f ]. % 51.50/51.67 apply (zenon_L153_); trivial. % 51.50/51.67 apply (zenon_L154_); trivial. % 51.50/51.67 apply (zenon_L156_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_L233_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2b1); [ zenon_intro zenon_H266 | zenon_intro zenon_H1fe ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H237 | zenon_intro zenon_H2a8 ]. % 51.50/51.67 apply (zenon_L245_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a8); [ zenon_intro zenon_H25e | zenon_intro zenon_H2a9 ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H237 | zenon_intro zenon_H2aa ]. % 51.50/51.67 apply (zenon_L196_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2aa); [ zenon_intro zenon_H280 | zenon_intro zenon_H2ab ]. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28d); [ zenon_intro zenon_H15f | zenon_intro zenon_H28f ]. % 51.50/51.67 apply (zenon_L116_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H28f); [ zenon_intro zenon_H165 | zenon_intro zenon_H290 ]. % 51.50/51.67 apply (zenon_L117_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H290); [ zenon_intro zenon_H169 | zenon_intro zenon_H175 ]. % 51.50/51.67 apply (zenon_L118_); trivial. % 51.50/51.67 apply (zenon_L831_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2ab); [ zenon_intro zenon_H26e | zenon_intro zenon_H218 ]. % 51.50/51.67 apply (zenon_L256_); trivial. % 51.50/51.67 apply (zenon_L156_); trivial. % 51.50/51.67 apply (zenon_or_s _ _ zenon_H2a9); [ zenon_intro zenon_H293 | zenon_intro zenon_H295 ]. % 51.50/51.67 apply (zenon_L233_); trivial. % 51.50/51.67 apply (zenon_L234_); trivial. % 51.50/51.67 apply (zenon_L151_); trivial. % 51.50/51.67 apply (zenon_L183_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H533); [ zenon_intro zenon_H413 | zenon_intro zenon_H534 ]. % 51.50/51.67 apply (zenon_L840_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H534); [ zenon_intro zenon_H419 | zenon_intro zenon_H535 ]. % 51.50/51.67 apply (zenon_L841_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H535); [ zenon_intro zenon_H41b | zenon_intro zenon_H536 ]. % 51.50/51.67 apply (zenon_L842_); trivial. % 51.50/51.67 apply (zenon_notand_s _ _ zenon_H536); [ zenon_intro zenon_H41f | zenon_intro zenon_H425 ]. % 51.50/51.67 apply (zenon_L843_); trivial. % 51.50/51.67 apply (zenon_L844_); trivial. % 51.50/51.67 Qed. % 51.50/51.67 % SZS output end Proof % 51.50/51.67 (* END-PROOF *) % 51.50/51.67 nodes searched: 1818021 % 51.50/51.67 max branch formulas: 2197 % 51.50/51.67 proof nodes created: 31220 % 51.50/51.67 formulas created: 1019749 % 51.50/51.67 %------------------------------------------------------------------------------