%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG115+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n025.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 25.56s 25.77s % Output : Proof 25.56s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : ALG115+1 : TPTP v8.1.0. Released v2.7.0. % 0.07/0.13 % Command : run_zenon %s %d % 0.12/0.34 % Computer : n025.cluster.edu % 0.12/0.34 % Model : x86_64 x86_64 % 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.34 % Memory : 8042.1875MB % 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.34 % CPULimit : 300 % 0.12/0.34 % WCLimit : 600 % 0.12/0.34 % DateTime : Wed Jun 8 06:55:49 EDT 2022 % 0.12/0.34 % CPUTime : % 25.56/25.77 (* PROOF-FOUND *) % 25.56/25.77 % SZS status Theorem % 25.56/25.77 (* BEGIN-PROOF *) % 25.56/25.77 % SZS output start Proof % 25.56/25.77 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))))))))))))))))))))))))))). % 25.56/25.77 Proof. % 25.56/25.77 assert (zenon_L1_ : (~((h4 (e10)) = (e20))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H12 zenon_H13 zenon_H14. % 25.56/25.77 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((h4 (e10)) = (e20))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H12. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H13. % 25.56/25.77 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 25.56/25.77 cut (((h4 (e10)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 25.56/25.77 congruence. % 25.56/25.77 apply zenon_H16. apply refl_equal. % 25.56/25.77 apply zenon_H15. apply sym_equal. exact zenon_H14. % 25.56/25.77 (* end of lemma zenon_L1_ *) % 25.56/25.77 assert (zenon_L2_ : (~((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H17 zenon_H18 zenon_H19. % 25.56/25.77 cut (((op1 (op1 (e13) (e13)) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 25.56/25.77 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 25.56/25.77 congruence. % 25.56/25.77 apply zenon_H1b. apply sym_equal. exact zenon_H19. % 25.56/25.77 apply zenon_H1a. apply sym_equal. exact zenon_H18. % 25.56/25.77 (* end of lemma zenon_L2_ *) % 25.56/25.77 assert (zenon_L3_ : (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((op1 (e11) (e11)) = (e10)) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H1c zenon_H1d zenon_H1e zenon_H18 zenon_H19. % 25.56/25.77 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e11) (e11)) = (op1 (e11) (e12)))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H1c. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H1d. % 25.56/25.77 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 25.56/25.77 cut (((e10) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 25.56/25.77 congruence. % 25.56/25.77 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H20 | zenon_intro zenon_H21 ]. % 25.56/25.77 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e10) = (op1 (e11) (e11)))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H1f. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H20. % 25.56/25.77 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 25.56/25.77 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 25.56/25.77 congruence. % 25.56/25.77 exact (zenon_H22 zenon_H1e). % 25.56/25.77 apply zenon_H21. apply refl_equal. % 25.56/25.77 apply zenon_H21. apply refl_equal. % 25.56/25.77 apply (zenon_L2_); trivial. % 25.56/25.77 (* end of lemma zenon_L3_ *) % 25.56/25.77 assert (zenon_L4_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((op1 (e12) (e12)) = (e10)) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H1d zenon_H23 zenon_H18 zenon_H19 zenon_H24. % 25.56/25.77 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 25.56/25.77 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e11) (e12)) = (op1 (e12) (e12)))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H24. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H25. % 25.56/25.77 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.77 cut (((op1 (e12) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 25.56/25.77 congruence. % 25.56/25.77 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e12) (e12)) = (op1 (e11) (e12)))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H27. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H1d. % 25.56/25.77 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 25.56/25.77 cut (((e10) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 25.56/25.77 congruence. % 25.56/25.77 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 25.56/25.77 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e10) = (op1 (e12) (e12)))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H28. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H25. % 25.56/25.77 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.77 cut (((op1 (e12) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 25.56/25.77 congruence. % 25.56/25.77 exact (zenon_H29 zenon_H23). % 25.56/25.77 apply zenon_H26. apply refl_equal. % 25.56/25.77 apply zenon_H26. apply refl_equal. % 25.56/25.77 apply (zenon_L2_); trivial. % 25.56/25.77 apply zenon_H26. apply refl_equal. % 25.56/25.77 apply zenon_H26. apply refl_equal. % 25.56/25.77 (* end of lemma zenon_L4_ *) % 25.56/25.77 assert (zenon_L5_ : (~((e13) = (e13))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H2a. % 25.56/25.77 apply zenon_H2a. apply refl_equal. % 25.56/25.77 (* end of lemma zenon_L5_ *) % 25.56/25.77 assert (zenon_L6_ : (~((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H2b zenon_H19. % 25.56/25.77 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 25.56/25.77 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 25.56/25.77 congruence. % 25.56/25.77 apply zenon_H1b. apply sym_equal. exact zenon_H19. % 25.56/25.77 apply zenon_H2a. apply refl_equal. % 25.56/25.77 (* end of lemma zenon_L6_ *) % 25.56/25.77 assert (zenon_L7_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e10) (e13)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H2c zenon_H18 zenon_H2d zenon_H19. % 25.56/25.77 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H2c. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H18. % 25.56/25.77 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 25.56/25.77 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2e]. % 25.56/25.77 congruence. % 25.56/25.77 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 25.56/25.77 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e12) = (op1 (e10) (e13)))). % 25.56/25.77 intro zenon_D_pnotp. % 25.56/25.77 apply zenon_H2e. % 25.56/25.77 rewrite <- zenon_D_pnotp. % 25.56/25.77 exact zenon_H2f. % 25.56/25.77 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 25.56/25.77 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H31]. % 25.56/25.77 congruence. % 25.56/25.77 exact (zenon_H31 zenon_H2d). % 25.56/25.77 apply zenon_H30. apply refl_equal. % 25.56/25.77 apply zenon_H30. apply refl_equal. % 25.56/25.77 apply (zenon_L6_); trivial. % 25.56/25.77 (* end of lemma zenon_L7_ *) % 25.56/25.77 assert (zenon_L8_ : (~((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e13)))) -> ((op1 (e13) (e13)) = (e10)) -> False). % 25.56/25.77 do 0 intro. intros zenon_H32 zenon_H33. % 25.56/25.77 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 25.56/25.77 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 25.56/25.77 congruence. % 25.56/25.77 exact (zenon_H34 zenon_H33). % 25.56/25.77 apply zenon_H2a. apply refl_equal. % 25.56/25.77 (* end of lemma zenon_L8_ *) % 25.56/25.77 assert (zenon_L9_ : ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e11) (e13)) = (e12)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 25.56/25.77 do 0 intro. intros zenon_H18 zenon_H35 zenon_H33 zenon_H2c. % 25.56/25.78 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H2c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H36. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H38]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e11) (e13)) = (op1 (e10) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H38. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H18. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 25.56/25.78 cut (((e12) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e12) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H39. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H36. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H3a zenon_H35). % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 apply (zenon_L8_); trivial. % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L9_ *) % 25.56/25.78 assert (zenon_L10_ : ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H18 zenon_H3b zenon_H33 zenon_H3c. % 25.56/25.78 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H3c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H3d. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3f]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e12) (e13)) = (op1 (e10) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H3f. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H18. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 25.56/25.78 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e12) = (op1 (e12) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H40. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H3d. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H41 zenon_H3b). % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply (zenon_L8_); trivial. % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L10_ *) % 25.56/25.78 assert (zenon_L11_ : ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e13)) = (e12)) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H18 zenon_H42 zenon_H33 zenon_H43. % 25.56/25.78 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H43. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H44. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e13) (e13)) = (op1 (e10) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H46. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H18. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 25.56/25.78 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e12) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H47. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H44. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H48 zenon_H42). % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply (zenon_L8_); trivial. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L11_ *) % 25.56/25.78 assert (zenon_L12_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e13)) = (e10)) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H33 zenon_H43. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H2d | zenon_intro zenon_H4a ]. % 25.56/25.78 apply (zenon_L7_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H35 | zenon_intro zenon_H4b ]. % 25.56/25.78 apply (zenon_L9_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H3b | zenon_intro zenon_H42 ]. % 25.56/25.78 apply (zenon_L10_); trivial. % 25.56/25.78 apply (zenon_L11_); trivial. % 25.56/25.78 (* end of lemma zenon_L12_ *) % 25.56/25.78 assert (zenon_L13_ : (~((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H4c zenon_H4d zenon_H4e. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H50. apply sym_equal. exact zenon_H4e. % 25.56/25.78 apply zenon_H4f. apply sym_equal. exact zenon_H4d. % 25.56/25.78 (* end of lemma zenon_L13_ *) % 25.56/25.78 assert (zenon_L14_ : (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e21) (e21)) = (e20)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H51 zenon_H14 zenon_H52 zenon_H4d zenon_H4e. % 25.56/25.78 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e21) (e21)) = (op2 (e21) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H51. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 25.56/25.78 cut (((e20) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e20) = (op2 (e21) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H53. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H54. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 25.56/25.78 cut (((op2 (e21) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H56]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H56 zenon_H52). % 25.56/25.78 apply zenon_H55. apply refl_equal. % 25.56/25.78 apply zenon_H55. apply refl_equal. % 25.56/25.78 apply (zenon_L13_); trivial. % 25.56/25.78 (* end of lemma zenon_L14_ *) % 25.56/25.78 assert (zenon_L15_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e22) (e22)) = (e20)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H14 zenon_H57 zenon_H4d zenon_H4e zenon_H58. % 25.56/25.78 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e21) (e22)) = (op2 (e22) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H58. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H59. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e22) (e22)) = (op2 (e21) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H5b. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 25.56/25.78 cut (((e20) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e20) = (op2 (e22) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H5c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H59. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H5d zenon_H57). % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply (zenon_L13_); trivial. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L15_ *) % 25.56/25.78 assert (zenon_L16_ : (~((e23) = (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H5e. % 25.56/25.78 apply zenon_H5e. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L16_ *) % 25.56/25.78 assert (zenon_L17_ : (~((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H5f zenon_H4e. % 25.56/25.78 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H50. apply sym_equal. exact zenon_H4e. % 25.56/25.78 apply zenon_H5e. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L17_ *) % 25.56/25.78 assert (zenon_L18_ : (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H60 zenon_H4d zenon_H61 zenon_H4e. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H60. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 25.56/25.78 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 25.56/25.78 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e22) = (op2 (e20) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H62. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H63. % 25.56/25.78 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 25.56/25.78 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H65 zenon_H61). % 25.56/25.78 apply zenon_H64. apply refl_equal. % 25.56/25.78 apply zenon_H64. apply refl_equal. % 25.56/25.78 apply (zenon_L17_); trivial. % 25.56/25.78 (* end of lemma zenon_L18_ *) % 25.56/25.78 assert (zenon_L19_ : (~((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e23)))) -> ((op2 (e23) (e23)) = (e20)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H66 zenon_H67. % 25.56/25.78 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H68 zenon_H67). % 25.56/25.78 apply zenon_H5e. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L19_ *) % 25.56/25.78 assert (zenon_L20_ : ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e23) (e23)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H4d zenon_H69 zenon_H67 zenon_H60. % 25.56/25.78 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H6a | zenon_intro zenon_H6b ]. % 25.56/25.78 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H60. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H6a. % 25.56/25.78 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 25.56/25.78 cut (((op2 (e21) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e21) (e23)) = (op2 (e20) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H6c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 25.56/25.78 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H6a | zenon_intro zenon_H6b ]. % 25.56/25.78 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e22) = (op2 (e21) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H6d. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H6a. % 25.56/25.78 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 25.56/25.78 cut (((op2 (e21) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H6e zenon_H69). % 25.56/25.78 apply zenon_H6b. apply refl_equal. % 25.56/25.78 apply zenon_H6b. apply refl_equal. % 25.56/25.78 apply (zenon_L19_); trivial. % 25.56/25.78 apply zenon_H6b. apply refl_equal. % 25.56/25.78 apply zenon_H6b. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L20_ *) % 25.56/25.78 assert (zenon_L21_ : ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e23) (e23)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H4d zenon_H6f zenon_H67 zenon_H70. % 25.56/25.78 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 25.56/25.78 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H70. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H71. % 25.56/25.78 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 25.56/25.78 cut (((op2 (e22) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e22) (e23)) = (op2 (e20) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H73. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 25.56/25.78 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 25.56/25.78 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e22) = (op2 (e22) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H74. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H71. % 25.56/25.78 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 25.56/25.78 cut (((op2 (e22) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H75 zenon_H6f). % 25.56/25.78 apply zenon_H72. apply refl_equal. % 25.56/25.78 apply zenon_H72. apply refl_equal. % 25.56/25.78 apply (zenon_L19_); trivial. % 25.56/25.78 apply zenon_H72. apply refl_equal. % 25.56/25.78 apply zenon_H72. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L21_ *) % 25.56/25.78 assert (zenon_L22_ : ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e23)) = (e22)) -> ((op2 (e23) (e23)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H4d zenon_H76 zenon_H67 zenon_H77. % 25.56/25.78 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H77. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H78. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e23) (e23)) = (op2 (e20) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H7a. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 25.56/25.78 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((e22) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H7b. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H78. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H7c zenon_H76). % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply (zenon_L19_); trivial. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L22_ *) % 25.56/25.78 assert (zenon_L23_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e23)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H67 zenon_H77. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H61 | zenon_intro zenon_H7e ]. % 25.56/25.78 apply (zenon_L18_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H69 | zenon_intro zenon_H7f ]. % 25.56/25.78 apply (zenon_L20_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H6f | zenon_intro zenon_H76 ]. % 25.56/25.78 apply (zenon_L21_); trivial. % 25.56/25.78 apply (zenon_L22_); trivial. % 25.56/25.78 (* end of lemma zenon_L23_ *) % 25.56/25.78 assert (zenon_L24_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H80 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_H81 zenon_H13 zenon_H82 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.78 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H81. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H13. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 25.56/25.78 cut (((h4 (e10)) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H88]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [ zenon_intro zenon_H89 | zenon_intro zenon_H8a ]. % 25.56/25.78 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10)))) = ((h4 (e10)) = (h4 (op1 (e10) (e10))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H88. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H89. % 25.56/25.78 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H8a]. % 25.56/25.78 cut (((h4 (op1 (e10) (e10))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H8b]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e10) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H8c zenon_H86). % 25.56/25.78 apply zenon_H8a. apply refl_equal. % 25.56/25.78 apply zenon_H8a. apply refl_equal. % 25.56/25.78 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H8d | zenon_intro zenon_H8e ]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (h4 (e10)) (h4 (e10))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H87. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H8d. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (h4 (e10)) (h4 (e10))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H8f. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H84. % 25.56/25.78 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 25.56/25.78 cut (((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H8d | zenon_intro zenon_H8e ]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H91. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H8d. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H92]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.78 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L1_); trivial. % 25.56/25.78 apply (zenon_L1_); trivial. % 25.56/25.78 apply zenon_H8e. apply refl_equal. % 25.56/25.78 apply zenon_H8e. apply refl_equal. % 25.56/25.78 exact (zenon_H90 zenon_H14). % 25.56/25.78 apply zenon_H8e. apply refl_equal. % 25.56/25.78 apply zenon_H8e. apply refl_equal. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.78 apply (zenon_L3_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.78 apply (zenon_L4_); trivial. % 25.56/25.78 apply (zenon_L12_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.78 apply (zenon_L14_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.78 apply (zenon_L15_); trivial. % 25.56/25.78 apply (zenon_L23_); trivial. % 25.56/25.78 (* end of lemma zenon_L24_ *) % 25.56/25.78 assert (zenon_L25_ : (~((e20) = (e20))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H95. % 25.56/25.78 apply zenon_H95. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L25_ *) % 25.56/25.78 assert (zenon_L26_ : ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e20)) = (e22)) -> (~((e20) = (e22))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H84 zenon_H96 zenon_H97. % 25.56/25.78 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H98 | zenon_intro zenon_H99 ]. % 25.56/25.78 cut (((e22) = (e22)) = ((e20) = (e22))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H97. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H98. % 25.56/25.78 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 25.56/25.78 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H9a]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op2 (e20) (e20)) = (e20)) = ((e22) = (e20))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H9a. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H84. % 25.56/25.78 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 25.56/25.78 cut (((op2 (e20) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H9b]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H9b zenon_H96). % 25.56/25.78 apply zenon_H95. apply refl_equal. % 25.56/25.78 apply zenon_H99. apply refl_equal. % 25.56/25.78 apply zenon_H99. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L26_ *) % 25.56/25.78 assert (zenon_L27_ : (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e21) (e21)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H9c zenon_H4d zenon_H9d zenon_H4e. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e21) (e21)) = (op2 (e21) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H9c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 25.56/25.78 cut (((e22) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e22) = (op2 (e21) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H9e. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H54. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 25.56/25.78 cut (((op2 (e21) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H9f zenon_H9d). % 25.56/25.78 apply zenon_H55. apply refl_equal. % 25.56/25.78 apply zenon_H55. apply refl_equal. % 25.56/25.78 apply (zenon_L17_); trivial. % 25.56/25.78 (* end of lemma zenon_L27_ *) % 25.56/25.78 assert (zenon_L28_ : (~((e10) = (e10))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Ha0. % 25.56/25.78 apply zenon_Ha0. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L28_ *) % 25.56/25.78 assert (zenon_L29_ : ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e10)) = (e12)) -> (~((e10) = (e12))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H86 zenon_Ha1 zenon_Ha2. % 25.56/25.78 elim (classic ((e12) = (e12))); [ zenon_intro zenon_Ha3 | zenon_intro zenon_Ha4 ]. % 25.56/25.78 cut (((e12) = (e12)) = ((e10) = (e12))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Ha2. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Ha3. % 25.56/25.78 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 25.56/25.78 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e10) (e10)) = (e10)) = ((e12) = (e10))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Ha5. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H86. % 25.56/25.78 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 25.56/25.78 cut (((op1 (e10) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Ha6 zenon_Ha1). % 25.56/25.78 apply zenon_Ha0. apply refl_equal. % 25.56/25.78 apply zenon_Ha4. apply refl_equal. % 25.56/25.78 apply zenon_Ha4. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L29_ *) % 25.56/25.78 assert (zenon_L30_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e11) (e11)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Ha7 zenon_H18 zenon_Ha8 zenon_H19. % 25.56/25.78 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e11) (e11)) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Ha7. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H18. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 25.56/25.78 cut (((e12) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H20 | zenon_intro zenon_H21 ]. % 25.56/25.78 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e12) = (op1 (e11) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Ha9. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H20. % 25.56/25.78 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 25.56/25.78 cut (((op1 (e11) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Haa]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Haa zenon_Ha8). % 25.56/25.78 apply zenon_H21. apply refl_equal. % 25.56/25.78 apply zenon_H21. apply refl_equal. % 25.56/25.78 apply (zenon_L6_); trivial. % 25.56/25.78 (* end of lemma zenon_L30_ *) % 25.56/25.78 assert (zenon_L31_ : (~((h4 (e11)) = (e21))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Hab zenon_Hac zenon_H4e. % 25.56/25.78 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (e11)) = (e21))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hab. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hac. % 25.56/25.78 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 25.56/25.78 cut (((h4 (e11)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_Had]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_Had. apply refl_equal. % 25.56/25.78 apply zenon_H50. apply sym_equal. exact zenon_H4e. % 25.56/25.78 (* end of lemma zenon_L31_ *) % 25.56/25.78 assert (zenon_L32_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Hae zenon_Haf zenon_Hb0. % 25.56/25.78 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hb0. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H25. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hb1. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hae. % 25.56/25.78 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 apply zenon_Hb2. apply sym_equal. exact zenon_Haf. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L32_ *) % 25.56/25.78 assert (zenon_L33_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Hb3 zenon_Hb4 zenon_Hb5. % 25.56/25.78 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hb5. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H59. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hb6. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hb3. % 25.56/25.78 cut (((e22) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply zenon_Hb7. apply sym_equal. exact zenon_Hb4. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L33_ *) % 25.56/25.78 assert (zenon_L34_ : ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e13)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H18 zenon_H42 zenon_H19 zenon_Hb8. % 25.56/25.78 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hb8. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H44. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e13) (e13)) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hb9. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H18. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 25.56/25.78 cut (((e12) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H47]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((e12) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H47. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H44. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H48 zenon_H42). % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply (zenon_L6_); trivial. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L34_ *) % 25.56/25.78 assert (zenon_L35_ : ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e23)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H4d zenon_H76 zenon_H4e zenon_Hba. % 25.56/25.78 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hba. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H78. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e23) (e23)) = (op2 (e21) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hbb. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 25.56/25.78 cut (((e22) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H7b]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((e22) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H7b. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H78. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H7c zenon_H76). % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply (zenon_L17_); trivial. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L35_ *) % 25.56/25.78 assert (zenon_L36_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H80 zenon_Hba zenon_H82 zenon_Hb8 zenon_Hbc zenon_H97 zenon_Hb0 zenon_Hbd zenon_Hbe zenon_H13 zenon_Hac zenon_Ha2 zenon_Hbf zenon_Hb5 zenon_Ha7 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43 zenon_H9c zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.78 apply (zenon_L26_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.78 apply (zenon_L27_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.78 apply (zenon_L29_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.78 apply (zenon_L30_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc6 ]. % 25.56/25.78 apply (zenon_L26_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc9 ]. % 25.56/25.78 apply (zenon_L29_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hca ]. % 25.56/25.78 cut (((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hbd. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hbe. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 25.56/25.78 cut (((h4 (e12)) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hcd]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [ zenon_intro zenon_Hce | zenon_intro zenon_Hcf ]. % 25.56/25.78 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11)))) = ((h4 (e12)) = (h4 (op1 (e10) (e11))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hcd. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hce. % 25.56/25.78 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hcf]. % 25.56/25.78 cut (((h4 (op1 (e10) (e11))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd1]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Hd1 zenon_Hcb). % 25.56/25.78 apply zenon_Hcf. apply refl_equal. % 25.56/25.78 apply zenon_Hcf. apply refl_equal. % 25.56/25.78 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd3 ]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e10)) (h4 (e11))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hcc. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hd2. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op2 (e20) (e21)) = (e22)) = ((op2 (h4 (e10)) (h4 (e11))) = (op2 (op2 (e23) (e23)) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hd4. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hc8. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 25.56/25.78 cut (((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_Hd2 | zenon_intro zenon_Hd3 ]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hd6. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hd2. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_Hd3]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 25.56/25.78 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L1_); trivial. % 25.56/25.78 apply (zenon_L31_); trivial. % 25.56/25.78 apply zenon_Hd3. apply refl_equal. % 25.56/25.78 apply zenon_Hd3. apply refl_equal. % 25.56/25.78 exact (zenon_Hd5 zenon_H4d). % 25.56/25.78 apply zenon_Hd3. apply refl_equal. % 25.56/25.78 apply zenon_Hd3. apply refl_equal. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Haf | zenon_intro zenon_H2d ]. % 25.56/25.78 apply (zenon_L32_); trivial. % 25.56/25.78 apply (zenon_L7_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H61 ]. % 25.56/25.78 apply (zenon_L33_); trivial. % 25.56/25.78 apply (zenon_L18_); trivial. % 25.56/25.78 apply (zenon_L34_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.78 apply (zenon_L3_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.78 apply (zenon_L4_); trivial. % 25.56/25.78 apply (zenon_L12_); trivial. % 25.56/25.78 apply (zenon_L35_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.78 apply (zenon_L14_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.78 apply (zenon_L15_); trivial. % 25.56/25.78 apply (zenon_L23_); trivial. % 25.56/25.78 (* end of lemma zenon_L36_ *) % 25.56/25.78 assert (zenon_L37_ : ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e20)) = (e23)) -> (~((e20) = (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H84 zenon_Hd8 zenon_Hd9. % 25.56/25.78 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hda | zenon_intro zenon_H5e ]. % 25.56/25.78 cut (((e23) = (e23)) = ((e20) = (e23))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hd9. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hda. % 25.56/25.78 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.78 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op2 (e20) (e20)) = (e20)) = ((e23) = (e20))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hdb. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H84. % 25.56/25.78 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 25.56/25.78 cut (((op2 (e20) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Hdc zenon_Hd8). % 25.56/25.78 apply zenon_H95. apply refl_equal. % 25.56/25.78 apply zenon_H5e. apply refl_equal. % 25.56/25.78 apply zenon_H5e. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L37_ *) % 25.56/25.78 assert (zenon_L38_ : ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e10)) = (e13)) -> (~((e10) = (e13))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H86 zenon_Hdd zenon_Hde. % 25.56/25.78 elim (classic ((e13) = (e13))); [ zenon_intro zenon_Hdf | zenon_intro zenon_H2a ]. % 25.56/25.78 cut (((e13) = (e13)) = ((e10) = (e13))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hde. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hdf. % 25.56/25.78 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 25.56/25.78 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_He0]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e10) (e10)) = (e10)) = ((e13) = (e10))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_He0. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H86. % 25.56/25.78 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 25.56/25.78 cut (((op1 (e10) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_He1 zenon_Hdd). % 25.56/25.78 apply zenon_Ha0. apply refl_equal. % 25.56/25.78 apply zenon_H2a. apply refl_equal. % 25.56/25.78 apply zenon_H2a. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L38_ *) % 25.56/25.78 assert (zenon_L39_ : (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e21) (e20)) = (e20)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_He2 zenon_H14 zenon_He3 zenon_H4d zenon_H4e. % 25.56/25.78 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e21) (e20)) = (op2 (e21) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_He2. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 25.56/25.78 cut (((e20) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He4]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_He5 | zenon_intro zenon_He6 ]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e20) = (op2 (e21) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_He4. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_He5. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_He7]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_He7 zenon_He3). % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 apply (zenon_L13_); trivial. % 25.56/25.78 (* end of lemma zenon_L39_ *) % 25.56/25.78 assert (zenon_L40_ : (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e21) (e20)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_He8 zenon_H4d zenon_He9 zenon_H4e. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e21) (e20)) = (op2 (e21) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_He8. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 25.56/25.78 cut (((e22) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hea]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_He5 | zenon_intro zenon_He6 ]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e22) = (op2 (e21) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hea. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_He5. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Heb]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Heb zenon_He9). % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 apply (zenon_L17_); trivial. % 25.56/25.78 (* end of lemma zenon_L40_ *) % 25.56/25.78 assert (zenon_L41_ : (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e21) (e22)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Hec zenon_H4d zenon_Hed zenon_H4e. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e21) (e22)) = (op2 (e21) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hec. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 25.56/25.78 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hee]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e22) = (op2 (e21) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hee. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hef. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 25.56/25.78 cut (((op2 (e21) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Hf1 zenon_Hed). % 25.56/25.78 apply zenon_Hf0. apply refl_equal. % 25.56/25.78 apply zenon_Hf0. apply refl_equal. % 25.56/25.78 apply (zenon_L17_); trivial. % 25.56/25.78 (* end of lemma zenon_L41_ *) % 25.56/25.78 assert (zenon_L42_ : ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e23) (e23)) = (op2 (e21) (e20)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H4e zenon_Hf2 zenon_Hf3. % 25.56/25.78 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_He5 | zenon_intro zenon_He6 ]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((op2 (e23) (e23)) = (op2 (e21) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hf3. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_He5. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hf4. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4e. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((e21) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_He5 | zenon_intro zenon_He6 ]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e21) = (op2 (e21) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hf5. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_He5. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Hf6 zenon_Hf2). % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 apply zenon_He6. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L42_ *) % 25.56/25.78 assert (zenon_L43_ : ((op2 (e22) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Hf7 zenon_H4e zenon_Hf2 zenon_Hf8. % 25.56/25.78 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 25.56/25.78 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((op2 (e21) (e20)) = (op2 (e22) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hf8. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hf9. % 25.56/25.78 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 25.56/25.78 cut (((op2 (e22) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e20)) = (op2 (e21) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hfb. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4e. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 25.56/25.78 cut (((e21) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hfc]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_Hf9 | zenon_intro zenon_Hfa ]. % 25.56/25.78 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e21) = (op2 (e22) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hfc. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hf9. % 25.56/25.78 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 25.56/25.78 cut (((op2 (e22) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_Hfd zenon_Hf7). % 25.56/25.78 apply zenon_Hfa. apply refl_equal. % 25.56/25.78 apply zenon_Hfa. apply refl_equal. % 25.56/25.78 apply (zenon_L42_); trivial. % 25.56/25.78 apply zenon_Hfa. apply refl_equal. % 25.56/25.78 apply zenon_Hfa. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L43_ *) % 25.56/25.78 assert (zenon_L44_ : ((op2 (e21) (e21)) = (e23)) -> ((op2 (e21) (e20)) = (e23)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Hfe zenon_Hff zenon_H100. % 25.56/25.78 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H54 | zenon_intro zenon_H55 ]. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (e21) (e20)) = (op2 (e21) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H100. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H54. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H101]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op2 (e21) (e21)) = (e23)) = ((op2 (e21) (e21)) = (op2 (e21) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H101. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hfe. % 25.56/25.78 cut (((e23) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H102]. % 25.56/25.78 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H55. apply refl_equal. % 25.56/25.78 apply zenon_H102. apply sym_equal. exact zenon_Hff. % 25.56/25.78 apply zenon_H55. apply refl_equal. % 25.56/25.78 apply zenon_H55. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L44_ *) % 25.56/25.78 assert (zenon_L45_ : (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e22))\/((op2 (e21) (e20)) = (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e22) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e21)) = (e23)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H103 zenon_H14 zenon_He2 zenon_Hf8 zenon_Hf7 zenon_H4e zenon_H4d zenon_He8 zenon_Hfe zenon_H100. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He3 | zenon_intro zenon_H104 ]. % 25.56/25.78 apply (zenon_L39_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H105 ]. % 25.56/25.78 apply (zenon_L43_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_He9 | zenon_intro zenon_Hff ]. % 25.56/25.78 apply (zenon_L40_); trivial. % 25.56/25.78 apply (zenon_L44_); trivial. % 25.56/25.78 (* end of lemma zenon_L45_ *) % 25.56/25.78 assert (zenon_L46_ : ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e10)) = (e11)) -> (~((e10) = (e11))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H86 zenon_H106 zenon_H107. % 25.56/25.78 elim (classic ((e11) = (e11))); [ zenon_intro zenon_H108 | zenon_intro zenon_H109 ]. % 25.56/25.78 cut (((e11) = (e11)) = ((e10) = (e11))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H107. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H108. % 25.56/25.78 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 25.56/25.78 cut (((e11) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e10) (e10)) = (e10)) = ((e11) = (e10))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H10a. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H86. % 25.56/25.78 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha0]. % 25.56/25.78 cut (((op1 (e10) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H10b]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H10b zenon_H106). % 25.56/25.78 apply zenon_Ha0. apply refl_equal. % 25.56/25.78 apply zenon_H109. apply refl_equal. % 25.56/25.78 apply zenon_H109. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L46_ *) % 25.56/25.78 assert (zenon_L47_ : (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((op1 (e11) (e10)) = (e10)) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H10c zenon_H1d zenon_H10d zenon_H18 zenon_H19. % 25.56/25.78 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H10c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1d. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 25.56/25.78 cut (((e10) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H10e]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e10) = (op1 (e11) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H10e. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H10f. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H111 zenon_H10d). % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 apply (zenon_L2_); trivial. % 25.56/25.78 (* end of lemma zenon_L47_ *) % 25.56/25.78 assert (zenon_L48_ : ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e13) (e13)) = (op1 (e11) (e10)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H19 zenon_H112 zenon_H113. % 25.56/25.78 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((op1 (e13) (e13)) = (op1 (e11) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H113. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H10f. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H114. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((e11) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e11) = (op1 (e11) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H115. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H10f. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H116 zenon_H112). % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L48_ *) % 25.56/25.78 assert (zenon_L49_ : ((op1 (e12) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H117 zenon_H19 zenon_H112 zenon_H118. % 25.56/25.78 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H119 | zenon_intro zenon_H11a ]. % 25.56/25.78 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((op1 (e11) (e10)) = (op1 (e12) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H118. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H119. % 25.56/25.78 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 25.56/25.78 cut (((op1 (e12) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H11b]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e10)) = (op1 (e11) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H11b. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 25.56/25.78 cut (((e11) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_H119 | zenon_intro zenon_H11a ]. % 25.56/25.78 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((e11) = (op1 (e12) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H11c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H119. % 25.56/25.78 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 25.56/25.78 cut (((op1 (e12) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H11d]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H11d zenon_H117). % 25.56/25.78 apply zenon_H11a. apply refl_equal. % 25.56/25.78 apply zenon_H11a. apply refl_equal. % 25.56/25.78 apply (zenon_L48_); trivial. % 25.56/25.78 apply zenon_H11a. apply refl_equal. % 25.56/25.78 apply zenon_H11a. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L49_ *) % 25.56/25.78 assert (zenon_L50_ : (~((h4 (e12)) = (e22))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H11e zenon_Hbe zenon_H4d. % 25.56/25.78 cut (((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (e12)) = (e22))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H11e. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hbe. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 25.56/25.78 cut (((h4 (e12)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H11f. apply refl_equal. % 25.56/25.78 apply zenon_H4f. apply sym_equal. exact zenon_H4d. % 25.56/25.78 (* end of lemma zenon_L50_ *) % 25.56/25.78 assert (zenon_L51_ : (~((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 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H120 zenon_Hac zenon_H121 zenon_H122 zenon_H4e zenon_H13 zenon_H14 zenon_Hbe zenon_H4d. % 25.56/25.78 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H120. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hac. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 25.56/25.78 cut (((h4 (e11)) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [ zenon_intro zenon_H125 | zenon_intro zenon_H126 ]. % 25.56/25.78 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12)))) = ((h4 (e11)) = (h4 (op1 (e10) (e12))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H124. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H125. % 25.56/25.78 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H126]. % 25.56/25.78 cut (((h4 (op1 (e10) (e12))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H127]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H128]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H128 zenon_H121). % 25.56/25.78 apply zenon_H126. apply refl_equal. % 25.56/25.78 apply zenon_H126. apply refl_equal. % 25.56/25.78 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H129 | zenon_intro zenon_H12a ]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H123. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H129. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H12b. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H122. % 25.56/25.78 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 25.56/25.78 cut (((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H129 | zenon_intro zenon_H12a ]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H12d. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H129. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 25.56/25.78 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H12e]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 25.56/25.78 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L1_); trivial. % 25.56/25.78 apply (zenon_L50_); trivial. % 25.56/25.78 apply zenon_H12a. apply refl_equal. % 25.56/25.78 apply zenon_H12a. apply refl_equal. % 25.56/25.78 exact (zenon_H12c zenon_H4e). % 25.56/25.78 apply zenon_H12a. apply refl_equal. % 25.56/25.78 apply zenon_H12a. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L51_ *) % 25.56/25.78 assert (zenon_L52_ : (~((op1 (e13) (e13)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e11)) = (e11)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H12f zenon_H112 zenon_H19 zenon_H130. % 25.56/25.78 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e13) (e13)) = (op1 (e12) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H12f. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H112. % 25.56/25.78 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H44 | zenon_intro zenon_H45 ]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H114. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H44. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L48_); trivial. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 apply zenon_H131. apply sym_equal. exact zenon_H130. % 25.56/25.78 (* end of lemma zenon_L52_ *) % 25.56/25.78 assert (zenon_L53_ : ((op1 (e12) (e12)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e11) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H132 zenon_H130 zenon_H112 zenon_H19 zenon_H133. % 25.56/25.78 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e12) (e11)) = (op1 (e12) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H133. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H25. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e12)) = (op1 (e12) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H134. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 25.56/25.78 cut (((e11) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H135]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((e11) = (op1 (e12) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H135. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H25. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H136 zenon_H132). % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 apply (zenon_L52_); trivial. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L53_ *) % 25.56/25.78 assert (zenon_L54_ : (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e12)) = (e11)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H137 zenon_H19 zenon_H138. % 25.56/25.78 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e12)) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H137. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H13a | zenon_intro zenon_H13b ]. % 25.56/25.78 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e11) = (op1 (e13) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H139. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H13a. % 25.56/25.78 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 25.56/25.78 cut (((op1 (e13) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H13c zenon_H138). % 25.56/25.78 apply zenon_H13b. apply refl_equal. % 25.56/25.78 apply zenon_H13b. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L54_ *) % 25.56/25.78 assert (zenon_L55_ : (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (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)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H13d zenon_H4d zenon_Hbe zenon_H14 zenon_H13 zenon_H4e zenon_H122 zenon_Hac zenon_H120 zenon_H10c zenon_H133 zenon_H112 zenon_H130 zenon_H137 zenon_H19. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H121 | zenon_intro zenon_H13e ]. % 25.56/25.78 apply (zenon_L51_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H13e); [ zenon_intro zenon_H140 | zenon_intro zenon_H13f ]. % 25.56/25.78 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H141 | zenon_intro zenon_H142 ]. % 25.56/25.78 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H10c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H141. % 25.56/25.78 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 25.56/25.78 cut (((op1 (e11) (e12)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e11) (e12)) = (op1 (e11) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H143. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 25.56/25.78 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H144]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H141 | zenon_intro zenon_H142 ]. % 25.56/25.78 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e11) = (op1 (e11) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H144. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H141. % 25.56/25.78 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 25.56/25.78 cut (((op1 (e11) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H145 zenon_H140). % 25.56/25.78 apply zenon_H142. apply refl_equal. % 25.56/25.78 apply zenon_H142. apply refl_equal. % 25.56/25.78 apply (zenon_L48_); trivial. % 25.56/25.78 apply zenon_H142. apply refl_equal. % 25.56/25.78 apply zenon_H142. apply refl_equal. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H13f); [ zenon_intro zenon_H132 | zenon_intro zenon_H138 ]. % 25.56/25.78 apply (zenon_L53_); trivial. % 25.56/25.78 apply (zenon_L54_); trivial. % 25.56/25.78 (* end of lemma zenon_L55_ *) % 25.56/25.78 assert (zenon_L56_ : (~((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e10) (e10)))) -> ((op1 (e11) (e12)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e10) (e10)) = (e10)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H146 zenon_H147 zenon_H19 zenon_H18 zenon_H86. % 25.56/25.78 cut (((op1 (e11) (e12)) = (e10)) = ((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e10) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H146. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H147. % 25.56/25.78 cut (((e10) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H148]. % 25.56/25.78 cut (((op1 (e11) (e12)) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ]. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e11) (e12)) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H149. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14a. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L2_); trivial. % 25.56/25.78 apply zenon_H14b. apply refl_equal. % 25.56/25.78 apply zenon_H14b. apply refl_equal. % 25.56/25.78 apply zenon_H148. apply sym_equal. exact zenon_H86. % 25.56/25.78 (* end of lemma zenon_L56_ *) % 25.56/25.78 assert (zenon_L57_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e10)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1d zenon_H14c zenon_H147 zenon_H86 zenon_H19 zenon_H18 zenon_H14d. % 25.56/25.78 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 25.56/25.78 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H14d. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14e. % 25.56/25.78 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 25.56/25.78 cut (((op1 (e13) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e13) (e10)) = (op1 (e10) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H150. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1d. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 25.56/25.78 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H151]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 25.56/25.78 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e10) = (op1 (e13) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H151. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14e. % 25.56/25.78 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 25.56/25.78 cut (((op1 (e13) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H152]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H152 zenon_H14c). % 25.56/25.78 apply zenon_H14f. apply refl_equal. % 25.56/25.78 apply zenon_H14f. apply refl_equal. % 25.56/25.78 apply (zenon_L56_); trivial. % 25.56/25.78 apply zenon_H14f. apply refl_equal. % 25.56/25.78 apply zenon_H14f. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L57_ *) % 25.56/25.78 assert (zenon_L58_ : (~((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e13) (e11)))) -> ((op1 (e11) (e12)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e11)) = (e10)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H153 zenon_H147 zenon_H19 zenon_H18 zenon_H154. % 25.56/25.78 cut (((op1 (e11) (e12)) = (e10)) = ((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e13) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H153. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H147. % 25.56/25.78 cut (((e10) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 25.56/25.78 cut (((op1 (e11) (e12)) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))); [ zenon_intro zenon_H14a | zenon_intro zenon_H14b ]. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e11) (e12)) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H149. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14a. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L2_); trivial. % 25.56/25.78 apply zenon_H14b. apply refl_equal. % 25.56/25.78 apply zenon_H14b. apply refl_equal. % 25.56/25.78 apply zenon_H155. apply sym_equal. exact zenon_H154. % 25.56/25.78 (* end of lemma zenon_L58_ *) % 25.56/25.78 assert (zenon_L59_ : (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((op1 (e12) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e13) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H156 zenon_H1d zenon_H157 zenon_H147 zenon_H154 zenon_H19 zenon_H18. % 25.56/25.78 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e12) (e11)) = (op1 (e13) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H156. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1d. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H153]. % 25.56/25.78 cut (((e10) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H158]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H159 | zenon_intro zenon_H15a ]. % 25.56/25.78 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e10) = (op1 (e12) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H158. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H159. % 25.56/25.78 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 25.56/25.78 cut (((op1 (e12) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H15b]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H15b zenon_H157). % 25.56/25.78 apply zenon_H15a. apply refl_equal. % 25.56/25.78 apply zenon_H15a. apply refl_equal. % 25.56/25.78 apply (zenon_L58_); trivial. % 25.56/25.78 (* end of lemma zenon_L59_ *) % 25.56/25.78 assert (zenon_L60_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((op1 (e13) (e12)) = (e10)) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1d zenon_H15c zenon_H18 zenon_H19 zenon_H15d. % 25.56/25.78 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H13a | zenon_intro zenon_H13b ]. % 25.56/25.78 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((op1 (e11) (e12)) = (op1 (e13) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H15d. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H13a. % 25.56/25.78 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 25.56/25.78 cut (((op1 (e13) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e13) (e12)) = (op1 (e11) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H15e. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1d. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 25.56/25.78 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H15f]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H13a | zenon_intro zenon_H13b ]. % 25.56/25.78 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e10) = (op1 (e13) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H15f. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H13a. % 25.56/25.78 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H13b]. % 25.56/25.78 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H160 zenon_H15c). % 25.56/25.78 apply zenon_H13b. apply refl_equal. % 25.56/25.78 apply zenon_H13b. apply refl_equal. % 25.56/25.78 apply (zenon_L2_); trivial. % 25.56/25.78 apply zenon_H13b. apply refl_equal. % 25.56/25.78 apply zenon_H13b. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L60_ *) % 25.56/25.78 assert (zenon_L61_ : (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e12) (e11)) = (e10)) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e11) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H161 zenon_H14d zenon_H86 zenon_H147 zenon_H157 zenon_H156 zenon_H15d zenon_H19 zenon_H1d zenon_H18 zenon_H35 zenon_H2c. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H14c | zenon_intro zenon_H162 ]. % 25.56/25.78 apply (zenon_L57_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H154 | zenon_intro zenon_H163 ]. % 25.56/25.78 apply (zenon_L59_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H15c | zenon_intro zenon_H33 ]. % 25.56/25.78 apply (zenon_L60_); trivial. % 25.56/25.78 apply (zenon_L9_); trivial. % 25.56/25.78 (* end of lemma zenon_L61_ *) % 25.56/25.78 assert (zenon_L62_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_Hae zenon_H164 zenon_H133. % 25.56/25.78 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H25 | zenon_intro zenon_H26 ]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e12) (e11)) = (op1 (e12) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H133. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H25. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e12) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H134. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hae. % 25.56/25.78 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 25.56/25.78 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 apply zenon_H165. apply sym_equal. exact zenon_H164. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 apply zenon_H26. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L62_ *) % 25.56/25.78 assert (zenon_L63_ : (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> ((op1 (e12) (e11)) = (e13)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H166 zenon_H167 zenon_H168. % 25.56/25.78 cut (((op1 (e11) (e11)) = (e13)) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H166. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H167. % 25.56/25.78 cut (((e13) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H169]. % 25.56/25.78 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H21. apply refl_equal. % 25.56/25.78 apply zenon_H169. apply sym_equal. exact zenon_H168. % 25.56/25.78 (* end of lemma zenon_L63_ *) % 25.56/25.78 assert (zenon_L64_ : (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e13)) = (e12)) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e12)) = (e10)) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e12)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H16a zenon_H2c zenon_H35 zenon_H18 zenon_H1d zenon_H15d zenon_H156 zenon_H147 zenon_H86 zenon_H14d zenon_H161 zenon_H19 zenon_H112 zenon_H132 zenon_H133 zenon_Hae zenon_H166 zenon_H167. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H157 | zenon_intro zenon_H16b ]. % 25.56/25.78 apply (zenon_L61_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H130 | zenon_intro zenon_H16c ]. % 25.56/25.78 apply (zenon_L53_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H164 | zenon_intro zenon_H168 ]. % 25.56/25.78 apply (zenon_L62_); trivial. % 25.56/25.78 apply (zenon_L63_); trivial. % 25.56/25.78 (* end of lemma zenon_L64_ *) % 25.56/25.78 assert (zenon_L65_ : ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e12) (e13)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H18 zenon_H3b zenon_H19 zenon_H16d. % 25.56/25.78 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e11) (e13)) = (op1 (e12) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H16d. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H3d. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16e]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e12) (e13)) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H16e. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H18. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 25.56/25.78 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e12) = (op1 (e12) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H40. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H3d. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H41 zenon_H3b). % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply (zenon_L6_); trivial. % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L65_ *) % 25.56/25.78 assert (zenon_L66_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e13)) = (e11)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H16f zenon_H19 zenon_H170. % 25.56/25.78 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H16f. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H3d | zenon_intro zenon_H3e ]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e11) = (op1 (e12) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H171. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H3d. % 25.56/25.78 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 25.56/25.78 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H172 zenon_H170). % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply zenon_H3e. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L66_ *) % 25.56/25.78 assert (zenon_L67_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1d zenon_H173 zenon_H18 zenon_H19 zenon_H174. % 25.56/25.78 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e11) (e12)) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H174. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H36. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H175]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) = ((op1 (e11) (e13)) = (op1 (e11) (e12)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H175. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1d. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H17]. % 25.56/25.78 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e10) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H176. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H36. % 25.56/25.78 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 25.56/25.78 cut (((op1 (e11) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H177 zenon_H173). % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 apply (zenon_L2_); trivial. % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 apply zenon_H37. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L67_ *) % 25.56/25.78 assert (zenon_L68_ : (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e11) (e10)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H178 zenon_H18 zenon_H179 zenon_H19. % 25.56/25.78 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e11) (e10)) = (op1 (e11) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H178. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H18. % 25.56/25.78 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 25.56/25.78 cut (((e12) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H10f | zenon_intro zenon_H110 ]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e12) = (op1 (e11) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H17a. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H10f. % 25.56/25.78 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 25.56/25.78 cut (((op1 (e11) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H17b zenon_H179). % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 apply zenon_H110. apply refl_equal. % 25.56/25.78 apply (zenon_L6_); trivial. % 25.56/25.78 (* end of lemma zenon_L68_ *) % 25.56/25.78 assert (zenon_L69_ : ((op1 (e11) (e11)) = (e13)) -> ((op1 (e11) (e10)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H167 zenon_H17c zenon_H17d. % 25.56/25.78 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H20 | zenon_intro zenon_H21 ]. % 25.56/25.78 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (e11) (e10)) = (op1 (e11) (e11)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H17d. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H20. % 25.56/25.78 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 25.56/25.78 cut (((op1 (e11) (e11)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H17e]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((op1 (e11) (e11)) = (e13)) = ((op1 (e11) (e11)) = (op1 (e11) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H17e. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H167. % 25.56/25.78 cut (((e13) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H17f]. % 25.56/25.78 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 25.56/25.78 congruence. % 25.56/25.78 apply zenon_H21. apply refl_equal. % 25.56/25.78 apply zenon_H17f. apply sym_equal. exact zenon_H17c. % 25.56/25.78 apply zenon_H21. apply refl_equal. % 25.56/25.78 apply zenon_H21. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L69_ *) % 25.56/25.78 assert (zenon_L70_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e12) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H180 zenon_H1d zenon_H10c zenon_H118 zenon_H117 zenon_H19 zenon_H18 zenon_H178 zenon_H167 zenon_H17d. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H180); [ zenon_intro zenon_H10d | zenon_intro zenon_H181 ]. % 25.56/25.78 apply (zenon_L47_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H181); [ zenon_intro zenon_H112 | zenon_intro zenon_H182 ]. % 25.56/25.78 apply (zenon_L49_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H179 | zenon_intro zenon_H17c ]. % 25.56/25.78 apply (zenon_L68_); trivial. % 25.56/25.78 apply (zenon_L69_); trivial. % 25.56/25.78 (* end of lemma zenon_L70_ *) % 25.56/25.78 assert (zenon_L71_ : (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e10)) = (e11)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H183 zenon_H19 zenon_H184. % 25.56/25.78 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H183. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19. % 25.56/25.78 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.78 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H14e | zenon_intro zenon_H14f ]. % 25.56/25.78 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e11) = (op1 (e13) (e10)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H185. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14e. % 25.56/25.78 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 25.56/25.78 cut (((op1 (e13) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H186]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H186 zenon_H184). % 25.56/25.78 apply zenon_H14f. apply refl_equal. % 25.56/25.78 apply zenon_H14f. apply refl_equal. % 25.56/25.78 apply zenon_H45. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L71_ *) % 25.56/25.78 assert (zenon_L72_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((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 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H187 zenon_H107 zenon_H174 zenon_H188 zenon_H137 zenon_H120 zenon_Hac zenon_H122 zenon_H4e zenon_H13 zenon_H14 zenon_Hbe zenon_H4d zenon_H13d zenon_Hb8 zenon_H16d zenon_H16a zenon_H2c zenon_H15d zenon_H156 zenon_H86 zenon_H14d zenon_H161 zenon_H133 zenon_Hae zenon_H166 zenon_H49 zenon_H16f zenon_H1c zenon_H189 zenon_H17d zenon_H167 zenon_H178 zenon_H18 zenon_H118 zenon_H10c zenon_H1d zenon_H180 zenon_H183 zenon_H19. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H106 | zenon_intro zenon_H18a ]. % 25.56/25.78 apply (zenon_L46_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H112 | zenon_intro zenon_H18b ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H10d | zenon_intro zenon_H18c ]. % 25.56/25.78 apply (zenon_L47_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H1e | zenon_intro zenon_H18d ]. % 25.56/25.78 apply (zenon_L3_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H147 | zenon_intro zenon_H173 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H188); [ zenon_intro zenon_H117 | zenon_intro zenon_H18e ]. % 25.56/25.78 apply (zenon_L49_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H130 | zenon_intro zenon_H18f ]. % 25.56/25.78 apply (zenon_L55_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H18f); [ zenon_intro zenon_H132 | zenon_intro zenon_H170 ]. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H2d | zenon_intro zenon_H4a ]. % 25.56/25.78 apply (zenon_L7_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H35 | zenon_intro zenon_H4b ]. % 25.56/25.78 apply (zenon_L64_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H3b | zenon_intro zenon_H42 ]. % 25.56/25.78 apply (zenon_L65_); trivial. % 25.56/25.78 apply (zenon_L34_); trivial. % 25.56/25.78 apply (zenon_L66_); trivial. % 25.56/25.78 apply (zenon_L67_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H117 | zenon_intro zenon_H184 ]. % 25.56/25.78 apply (zenon_L70_); trivial. % 25.56/25.78 apply (zenon_L71_); trivial. % 25.56/25.78 (* end of lemma zenon_L72_ *) % 25.56/25.78 assert (zenon_L73_ : ((op2 (e21) (e22)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H190 zenon_H4e zenon_Hf2 zenon_He2. % 25.56/25.78 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((op2 (e21) (e20)) = (op2 (e21) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_He2. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hef. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e21) (e22)) = (op2 (e21) (e20)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H191. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4e. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 25.56/25.78 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_Hef | zenon_intro zenon_Hf0 ]. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e21) = (op2 (e21) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H192. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hef. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 25.56/25.78 cut (((op2 (e21) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H193 zenon_H190). % 25.56/25.78 apply zenon_Hf0. apply refl_equal. % 25.56/25.78 apply zenon_Hf0. apply refl_equal. % 25.56/25.78 apply (zenon_L42_); trivial. % 25.56/25.78 apply zenon_Hf0. apply refl_equal. % 25.56/25.78 apply zenon_Hf0. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L73_ *) % 25.56/25.78 assert (zenon_L74_ : (~((op2 (e23) (e23)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H194 zenon_Hf2 zenon_H4e zenon_H195. % 25.56/25.78 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (e23) (e23)) = (op2 (e22) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H194. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_Hf2. % 25.56/25.78 cut (((e21) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 25.56/25.78 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H78 | zenon_intro zenon_H79 ]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_Hf4. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H78. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L42_); trivial. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 apply zenon_H196. apply sym_equal. exact zenon_H195. % 25.56/25.78 (* end of lemma zenon_L74_ *) % 25.56/25.78 assert (zenon_L75_ : ((op2 (e22) (e22)) = (e21)) -> ((op2 (e22) (e21)) = (e21)) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H197 zenon_H195 zenon_Hf2 zenon_H4e zenon_H198. % 25.56/25.78 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e22) (e21)) = (op2 (e22) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H198. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H59. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e22)) = (op2 (e22) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H199. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4e. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 25.56/25.78 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e21) = (op2 (e22) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H19a. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H59. % 25.56/25.78 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.78 cut (((op2 (e22) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H19b]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H19b zenon_H197). % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply (zenon_L74_); trivial. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 apply zenon_H5a. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L75_ *) % 25.56/25.78 assert (zenon_L76_ : (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e22)) = (e21)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H19c zenon_H4e zenon_H19d. % 25.56/25.78 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e22)) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H19c. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4e. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 25.56/25.78 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e21) = (op2 (e23) (e22)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H19e. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H19f. % 25.56/25.78 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 25.56/25.78 cut (((op2 (e23) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1a1]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H1a1 zenon_H19d). % 25.56/25.78 apply zenon_H1a0. apply refl_equal. % 25.56/25.78 apply zenon_H1a0. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L76_ *) % 25.56/25.78 assert (zenon_L77_ : (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e22) (e21)) = (e21)) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1a2 zenon_H19 zenon_H183 zenon_H180 zenon_H1d zenon_H10c zenon_H118 zenon_H18 zenon_H178 zenon_H167 zenon_H17d zenon_H189 zenon_H1c zenon_H16f zenon_H49 zenon_H166 zenon_Hae zenon_H133 zenon_H161 zenon_H14d zenon_H86 zenon_H156 zenon_H15d zenon_H2c zenon_H16a zenon_H16d zenon_Hb8 zenon_H13d zenon_H4d zenon_Hbe zenon_H14 zenon_H13 zenon_Hac zenon_H120 zenon_H137 zenon_H188 zenon_H174 zenon_H107 zenon_H187 zenon_He2 zenon_H198 zenon_Hf2 zenon_H195 zenon_H19c zenon_H4e. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H1a2); [ zenon_intro zenon_H122 | zenon_intro zenon_H1a3 ]. % 25.56/25.78 apply (zenon_L72_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H190 | zenon_intro zenon_H1a4 ]. % 25.56/25.78 apply (zenon_L73_); trivial. % 25.56/25.78 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H197 | zenon_intro zenon_H19d ]. % 25.56/25.78 apply (zenon_L75_); trivial. % 25.56/25.78 apply (zenon_L76_); trivial. % 25.56/25.78 (* end of lemma zenon_L77_ *) % 25.56/25.78 assert (zenon_L78_ : (~((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e23) (e21)))) -> ((op2 (e21) (e22)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e21)) = (e20)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1a5 zenon_H1a6 zenon_H4e zenon_H4d zenon_H1a7. % 25.56/25.78 cut (((op2 (e21) (e22)) = (e20)) = ((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e23) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1a5. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1a6. % 25.56/25.78 cut (((e20) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1a8]. % 25.56/25.78 cut (((op2 (e21) (e22)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1ab ]. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e21) (e22)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1a9. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1aa. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L13_); trivial. % 25.56/25.78 apply zenon_H1ab. apply refl_equal. % 25.56/25.78 apply zenon_H1ab. apply refl_equal. % 25.56/25.78 apply zenon_H1a8. apply sym_equal. exact zenon_H1a7. % 25.56/25.78 (* end of lemma zenon_L78_ *) % 25.56/25.78 assert (zenon_L79_ : (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e22) (e21)) = (e20)) -> ((op2 (e21) (e22)) = (e20)) -> ((op2 (e23) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1ac zenon_H14 zenon_H1ad zenon_H1a6 zenon_H1a7 zenon_H4e zenon_H4d. % 25.56/25.78 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e22) (e21)) = (op2 (e23) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1ac. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H14. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1a5]. % 25.56/25.78 cut (((e20) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H1af | zenon_intro zenon_H1b0 ]. % 25.56/25.78 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e20) = (op2 (e22) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1ae. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1af. % 25.56/25.78 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 25.56/25.78 cut (((op2 (e22) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H1b1 zenon_H1ad). % 25.56/25.78 apply zenon_H1b0. apply refl_equal. % 25.56/25.78 apply zenon_H1b0. apply refl_equal. % 25.56/25.78 apply (zenon_L78_); trivial. % 25.56/25.78 (* end of lemma zenon_L79_ *) % 25.56/25.78 assert (zenon_L80_ : (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e21)) = (e21)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1b2 zenon_H4e zenon_H1b3. % 25.56/25.78 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e21)) = (op2 (e23) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1b2. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4e. % 25.56/25.78 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.78 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1b6 ]. % 25.56/25.78 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e21) = (op2 (e23) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1b4. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1b5. % 25.56/25.78 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 25.56/25.78 cut (((op2 (e23) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H1b7 zenon_H1b3). % 25.56/25.78 apply zenon_H1b6. apply refl_equal. % 25.56/25.78 apply zenon_H1b6. apply refl_equal. % 25.56/25.78 apply zenon_H79. apply refl_equal. % 25.56/25.78 (* end of lemma zenon_L80_ *) % 25.56/25.78 assert (zenon_L81_ : (~((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e21)))) -> ((op2 (e21) (e23)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e22)) -> False). % 25.56/25.78 do 0 intro. intros zenon_H1b8 zenon_H69 zenon_H4e zenon_Hc8. % 25.56/25.78 cut (((op2 (e21) (e23)) = (e22)) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1b8. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H69. % 25.56/25.78 cut (((e22) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b9]. % 25.56/25.78 cut (((op2 (e21) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1ba]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1bc ]. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e21) (e23)) = (op2 (op2 (e23) (e23)) (e23)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1ba. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1bb. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 25.56/25.78 congruence. % 25.56/25.78 apply (zenon_L17_); trivial. % 25.56/25.78 apply zenon_H1bc. apply refl_equal. % 25.56/25.78 apply zenon_H1bc. apply refl_equal. % 25.56/25.78 apply zenon_H1b9. apply sym_equal. exact zenon_Hc8. % 25.56/25.78 (* end of lemma zenon_L81_ *) % 25.56/25.78 assert (zenon_L82_ : ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e21)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> False). % 25.56/25.78 do 0 intro. intros zenon_H4d zenon_H1bd zenon_H69 zenon_Hc8 zenon_H4e zenon_H1be. % 25.56/25.78 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1b6 ]. % 25.56/25.78 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e20) (e21)) = (op2 (e23) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1be. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1b5. % 25.56/25.78 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 25.56/25.78 cut (((op2 (e23) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 25.56/25.78 congruence. % 25.56/25.78 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e23) (e21)) = (op2 (e20) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1bf. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H4d. % 25.56/25.78 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 25.56/25.78 cut (((e22) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c0]. % 25.56/25.78 congruence. % 25.56/25.78 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H1b5 | zenon_intro zenon_H1b6 ]. % 25.56/25.78 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e22) = (op2 (e23) (e21)))). % 25.56/25.78 intro zenon_D_pnotp. % 25.56/25.78 apply zenon_H1c0. % 25.56/25.78 rewrite <- zenon_D_pnotp. % 25.56/25.78 exact zenon_H1b5. % 25.56/25.78 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 25.56/25.78 cut (((op2 (e23) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 25.56/25.78 congruence. % 25.56/25.78 exact (zenon_H1c1 zenon_H1bd). % 25.56/25.78 apply zenon_H1b6. apply refl_equal. % 25.56/25.79 apply zenon_H1b6. apply refl_equal. % 25.56/25.79 apply (zenon_L81_); trivial. % 25.56/25.79 apply zenon_H1b6. apply refl_equal. % 25.56/25.79 apply zenon_H1b6. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L82_ *) % 25.56/25.79 assert (zenon_L83_ : (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1c2 zenon_Hfe zenon_H1c3. % 25.56/25.79 cut (((op2 (e21) (e21)) = (e23)) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1c2. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hfe. % 25.56/25.79 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c4]. % 25.56/25.79 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H55. apply refl_equal. % 25.56/25.79 apply zenon_H1c4. apply sym_equal. exact zenon_H1c3. % 25.56/25.79 (* end of lemma zenon_L83_ *) % 25.56/25.79 assert (zenon_L84_ : (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> ((op2 (e21) (e22)) = (e20)) -> ((op2 (e22) (e21)) = (e20)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1c5 zenon_H1a6 zenon_H1ad zenon_H14 zenon_H1ac zenon_H1b2 zenon_H1be zenon_H4e zenon_Hc8 zenon_H69 zenon_H4d zenon_H1c2 zenon_Hfe. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1c6 ]. % 25.56/25.79 apply (zenon_L79_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1c7 ]. % 25.56/25.79 apply (zenon_L80_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1bd | zenon_intro zenon_H1c3 ]. % 25.56/25.79 apply (zenon_L82_); trivial. % 25.56/25.79 apply (zenon_L83_); trivial. % 25.56/25.79 (* end of lemma zenon_L84_ *) % 25.56/25.79 assert (zenon_L85_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_Hb3 zenon_H1c8 zenon_H198. % 25.56/25.79 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 25.56/25.79 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e22) (e21)) = (op2 (e22) (e22)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H198. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H59. % 25.56/25.79 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.79 cut (((op2 (e22) (e22)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e22) (e21)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H199. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hb3. % 25.56/25.79 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 25.56/25.79 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H5a. apply refl_equal. % 25.56/25.79 apply zenon_H1c9. apply sym_equal. exact zenon_H1c8. % 25.56/25.79 apply zenon_H5a. apply refl_equal. % 25.56/25.79 apply zenon_H5a. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L85_ *) % 25.56/25.79 assert (zenon_L86_ : (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> ((op2 (e22) (e21)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1ca zenon_Hfe zenon_H1cb. % 25.56/25.79 cut (((op2 (e21) (e21)) = (e23)) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1ca. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hfe. % 25.56/25.79 cut (((e23) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 25.56/25.79 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H55. apply refl_equal. % 25.56/25.79 apply zenon_H1cc. apply sym_equal. exact zenon_H1cb. % 25.56/25.79 (* end of lemma zenon_L86_ *) % 25.56/25.79 assert (zenon_L87_ : (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e21) (e22)) = (e20)) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e22) (e22)) = (e21)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1cd zenon_H1c2 zenon_H4d zenon_H69 zenon_Hc8 zenon_H1be zenon_H1b2 zenon_H1ac zenon_H14 zenon_H1a6 zenon_H1c5 zenon_H4e zenon_Hf2 zenon_H197 zenon_H198 zenon_Hb3 zenon_H1ca zenon_Hfe. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ce ]. % 25.56/25.79 apply (zenon_L84_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H195 | zenon_intro zenon_H1cf ]. % 25.56/25.79 apply (zenon_L75_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H1cb ]. % 25.56/25.79 apply (zenon_L85_); trivial. % 25.56/25.79 apply (zenon_L86_); trivial. % 25.56/25.79 (* end of lemma zenon_L87_ *) % 25.56/25.79 assert (zenon_L88_ : (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1d0 zenon_H4e zenon_H1d1. % 25.56/25.79 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1d0. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H4e. % 25.56/25.79 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.79 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1d2]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e21) = (op2 (e22) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1d2. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H71. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 25.56/25.79 cut (((op2 (e22) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1d3]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H1d3 zenon_H1d1). % 25.56/25.79 apply zenon_H72. apply refl_equal. % 25.56/25.79 apply zenon_H72. apply refl_equal. % 25.56/25.79 apply zenon_H79. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L88_ *) % 25.56/25.79 assert (zenon_L89_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H14 zenon_H1d4 zenon_H4d zenon_H4e zenon_Hec. % 25.56/25.79 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H6a | zenon_intro zenon_H6b ]. % 25.56/25.79 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e21) (e22)) = (op2 (e21) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_Hec. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H6a. % 25.56/25.79 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 25.56/25.79 cut (((op2 (e21) (e23)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e21) (e23)) = (op2 (e21) (e22)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1d5. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H14. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 25.56/25.79 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1d6]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H6a | zenon_intro zenon_H6b ]. % 25.56/25.79 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e20) = (op2 (e21) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1d6. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H6a. % 25.56/25.79 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 25.56/25.79 cut (((op2 (e21) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H1d7 zenon_H1d4). % 25.56/25.79 apply zenon_H6b. apply refl_equal. % 25.56/25.79 apply zenon_H6b. apply refl_equal. % 25.56/25.79 apply (zenon_L13_); trivial. % 25.56/25.79 apply zenon_H6b. apply refl_equal. % 25.56/25.79 apply zenon_H6b. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L89_ *) % 25.56/25.79 assert (zenon_L90_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e22))\/((op2 (e21) (e20)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> ((op2 (e21) (e21)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.79 do 0 intro. intros zenon_Hbc zenon_H97 zenon_H84 zenon_Hec zenon_H14 zenon_H1d8 zenon_H9c zenon_H1d9 zenon_H100 zenon_He8 zenon_Hf8 zenon_H103 zenon_H19c zenon_He2 zenon_H187 zenon_H107 zenon_H174 zenon_H188 zenon_H137 zenon_H120 zenon_Hac zenon_H13 zenon_Hbe zenon_H13d zenon_Hb8 zenon_H16d zenon_H16a zenon_H2c zenon_H15d zenon_H156 zenon_H86 zenon_H14d zenon_H161 zenon_H133 zenon_Hae zenon_H166 zenon_H49 zenon_H16f zenon_H1c zenon_H189 zenon_H17d zenon_H167 zenon_H178 zenon_H18 zenon_H118 zenon_H10c zenon_H1d zenon_H180 zenon_H183 zenon_H19 zenon_H1a2 zenon_Hfe zenon_H1ca zenon_H198 zenon_Hf2 zenon_H1c5 zenon_H1ac zenon_H1b2 zenon_H1be zenon_H1c2 zenon_H1cd zenon_H1d0 zenon_H51 zenon_H1da zenon_Hb5 zenon_Hb3 zenon_H60 zenon_H4d zenon_H4e. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc6 ]. % 25.56/25.79 apply (zenon_L26_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_He3 | zenon_intro zenon_H1db ]. % 25.56/25.79 apply (zenon_L39_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H52 | zenon_intro zenon_H1dc ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1d4 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_He9 | zenon_intro zenon_H1dd ]. % 25.56/25.79 apply (zenon_L40_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hed | zenon_intro zenon_H69 ]. % 25.56/25.79 apply (zenon_L41_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1d9); [ zenon_intro zenon_Hf7 | zenon_intro zenon_H1df ]. % 25.56/25.79 apply (zenon_L45_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H195 | zenon_intro zenon_H1e0 ]. % 25.56/25.79 apply (zenon_L77_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e0); [ zenon_intro zenon_H197 | zenon_intro zenon_H1d1 ]. % 25.56/25.79 apply (zenon_L87_); trivial. % 25.56/25.79 apply (zenon_L88_); trivial. % 25.56/25.79 apply (zenon_L89_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H61 ]. % 25.56/25.79 apply (zenon_L33_); trivial. % 25.56/25.79 apply (zenon_L18_); trivial. % 25.56/25.79 (* end of lemma zenon_L90_ *) % 25.56/25.79 assert (zenon_L91_ : (~((e12) = (e12))) -> False). % 25.56/25.79 do 0 intro. intros zenon_Ha4. % 25.56/25.79 apply zenon_Ha4. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L91_ *) % 25.56/25.79 assert (zenon_L92_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e12)) = (e13)) -> (~((e12) = (e13))) -> False). % 25.56/25.79 do 0 intro. intros zenon_Hae zenon_H1e1 zenon_H1e2. % 25.56/25.79 elim (classic ((e13) = (e13))); [ zenon_intro zenon_Hdf | zenon_intro zenon_H2a ]. % 25.56/25.79 cut (((e13) = (e13)) = ((e12) = (e13))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1e2. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hdf. % 25.56/25.79 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 25.56/25.79 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1e3]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e12) (e12)) = (e12)) = ((e13) = (e12))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1e3. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hae. % 25.56/25.79 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 25.56/25.79 cut (((op1 (e12) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1e4]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H1e4 zenon_H1e1). % 25.56/25.79 apply zenon_Ha4. apply refl_equal. % 25.56/25.79 apply zenon_H2a. apply refl_equal. % 25.56/25.79 apply zenon_H2a. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L92_ *) % 25.56/25.79 assert (zenon_L93_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e11) (e13)) = (e12)) -> ((op1 (e13) (e13)) = (e13)) -> False). % 25.56/25.79 do 0 intro. intros zenon_Hb8 zenon_H18 zenon_H35 zenon_H1e5. % 25.56/25.79 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_Hb8. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H18. % 25.56/25.79 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 25.56/25.79 cut (((e12) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H36 | zenon_intro zenon_H37 ]. % 25.56/25.79 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e12) = (op1 (e11) (e13)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H39. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H36. % 25.56/25.79 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 25.56/25.79 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H3a zenon_H35). % 25.56/25.79 apply zenon_H37. apply refl_equal. % 25.56/25.79 apply zenon_H37. apply refl_equal. % 25.56/25.79 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 25.56/25.79 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H1e7 zenon_H1e5). % 25.56/25.79 apply zenon_H2a. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L93_ *) % 25.56/25.79 assert (zenon_L94_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H49 zenon_H2c zenon_H1e5 zenon_H16d zenon_H18 zenon_H19 zenon_Hb8. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H2d | zenon_intro zenon_H4a ]. % 25.56/25.79 apply (zenon_L7_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H35 | zenon_intro zenon_H4b ]. % 25.56/25.79 apply (zenon_L93_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H3b | zenon_intro zenon_H42 ]. % 25.56/25.79 apply (zenon_L65_); trivial. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 (* end of lemma zenon_L94_ *) % 25.56/25.79 assert (zenon_L95_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e22))\/((op2 (e21) (e20)) = (e23))))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H82 zenon_Hb8 zenon_H1e8 zenon_Hde zenon_H100 zenon_Hfe zenon_He8 zenon_H4d zenon_H4e zenon_Hbc zenon_H97 zenon_H84 zenon_Hec zenon_H14 zenon_H1d8 zenon_H9c zenon_H1d9 zenon_Hf8 zenon_H103 zenon_H19c zenon_He2 zenon_H187 zenon_H107 zenon_H174 zenon_H188 zenon_H137 zenon_H120 zenon_Hac zenon_H13 zenon_Hbe zenon_H13d zenon_H16a zenon_H15d zenon_H156 zenon_H14d zenon_H161 zenon_H133 zenon_H166 zenon_H16f zenon_H189 zenon_H17d zenon_H178 zenon_H118 zenon_H10c zenon_H180 zenon_H183 zenon_H1a2 zenon_H1ca zenon_H198 zenon_H1c5 zenon_H1ac zenon_H1b2 zenon_H1be zenon_H1c2 zenon_H1cd zenon_H1d0 zenon_H51 zenon_H1da zenon_Hb5 zenon_Hb3 zenon_H60 zenon_H1e2 zenon_H16d zenon_Ha7 zenon_Ha2 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.79 apply (zenon_L29_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.79 apply (zenon_L30_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hdd | zenon_intro zenon_H1e9 ]. % 25.56/25.79 apply (zenon_L38_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H167 | zenon_intro zenon_H1ea ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He3 | zenon_intro zenon_H104 ]. % 25.56/25.79 apply (zenon_L39_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H105 ]. % 25.56/25.79 apply (zenon_L90_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_He9 | zenon_intro zenon_Hff ]. % 25.56/25.79 apply (zenon_L40_); trivial. % 25.56/25.79 apply (zenon_L44_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e5 ]. % 25.56/25.79 apply (zenon_L92_); trivial. % 25.56/25.79 apply (zenon_L94_); trivial. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 (* end of lemma zenon_L95_ *) % 25.56/25.79 assert (zenon_L96_ : (~((e22) = (e22))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H99. % 25.56/25.79 apply zenon_H99. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L96_ *) % 25.56/25.79 assert (zenon_L97_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e22) (e22)) = (e23)) -> (~((e22) = (e23))) -> False). % 25.56/25.79 do 0 intro. intros zenon_Hb3 zenon_H1eb zenon_H1ec. % 25.56/25.79 elim (classic ((e23) = (e23))); [ zenon_intro zenon_Hda | zenon_intro zenon_H5e ]. % 25.56/25.79 cut (((e23) = (e23)) = ((e22) = (e23))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1ec. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hda. % 25.56/25.79 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.79 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e22) (e22)) = (e22)) = ((e23) = (e22))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1ed. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hb3. % 25.56/25.79 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H99]. % 25.56/25.79 cut (((op2 (e22) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H1ee zenon_H1eb). % 25.56/25.79 apply zenon_H99. apply refl_equal. % 25.56/25.79 apply zenon_H5e. apply refl_equal. % 25.56/25.79 apply zenon_H5e. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L97_ *) % 25.56/25.79 assert (zenon_L98_ : (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e23) (e23)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_Hba zenon_H4d zenon_H69 zenon_H1ef. % 25.56/25.79 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_Hba. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H4d. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f0]. % 25.56/25.79 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H6a | zenon_intro zenon_H6b ]. % 25.56/25.79 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e22) = (op2 (e21) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H6d. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H6a. % 25.56/25.79 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 25.56/25.79 cut (((op2 (e21) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H6e zenon_H69). % 25.56/25.79 apply zenon_H6b. apply refl_equal. % 25.56/25.79 apply zenon_H6b. apply refl_equal. % 25.56/25.79 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.79 cut (((op2 (e23) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H1f1 zenon_H1ef). % 25.56/25.79 apply zenon_H5e. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L98_ *) % 25.56/25.79 assert (zenon_L99_ : ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e22) (e23)) = (e22)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H4d zenon_H6f zenon_H4e zenon_H1f2. % 25.56/25.79 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1f2. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H71. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((e22) = (op2 (op2 (e23) (e23)) (e23))) = ((op2 (e22) (e23)) = (op2 (e21) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1f3. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H4d. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H5f]. % 25.56/25.79 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H74]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H71 | zenon_intro zenon_H72 ]. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e22) = (op2 (e22) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H74. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H71. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 25.56/25.79 cut (((op2 (e22) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H75]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H75 zenon_H6f). % 25.56/25.79 apply zenon_H72. apply refl_equal. % 25.56/25.79 apply zenon_H72. apply refl_equal. % 25.56/25.79 apply (zenon_L17_); trivial. % 25.56/25.79 apply zenon_H72. apply refl_equal. % 25.56/25.79 apply zenon_H72. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L99_ *) % 25.56/25.79 assert (zenon_L100_ : (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e23) (e23)) = (e23)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H7d zenon_H60 zenon_H1ef zenon_H1f2 zenon_H4d zenon_H4e zenon_Hba. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H7d); [ zenon_intro zenon_H61 | zenon_intro zenon_H7e ]. % 25.56/25.79 apply (zenon_L18_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H7e); [ zenon_intro zenon_H69 | zenon_intro zenon_H7f ]. % 25.56/25.79 apply (zenon_L98_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H7f); [ zenon_intro zenon_H6f | zenon_intro zenon_H76 ]. % 25.56/25.79 apply (zenon_L99_); trivial. % 25.56/25.79 apply (zenon_L35_); trivial. % 25.56/25.79 (* end of lemma zenon_L100_ *) % 25.56/25.79 assert (zenon_L101_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e23) (e22)) = (e21))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (((op1 (e10) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e13) (e12)) = (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e22))\/((op2 (e21) (e20)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H80 zenon_Hba zenon_H1f4 zenon_Hd9 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_Hc0 zenon_Ha2 zenon_Ha7 zenon_H16d zenon_H1e2 zenon_Hb5 zenon_H1da zenon_H1d0 zenon_H1cd zenon_H1c2 zenon_H1be zenon_H1b2 zenon_H1ac zenon_H1c5 zenon_H198 zenon_H1ca zenon_H1a2 zenon_H183 zenon_H180 zenon_H10c zenon_H118 zenon_H178 zenon_H17d zenon_H189 zenon_H16f zenon_H166 zenon_H133 zenon_H161 zenon_H14d zenon_H156 zenon_H15d zenon_H16a zenon_H13d zenon_Hbe zenon_H13 zenon_Hac zenon_H120 zenon_H137 zenon_H188 zenon_H174 zenon_H107 zenon_H187 zenon_He2 zenon_H19c zenon_H103 zenon_Hf8 zenon_H1d9 zenon_H9c zenon_H1d8 zenon_Hec zenon_H97 zenon_Hbc zenon_He8 zenon_H100 zenon_Hde zenon_H1e8 zenon_Hb8 zenon_H82 zenon_H1ec zenon_H1f2 zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.79 apply (zenon_L26_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1f5 ]. % 25.56/25.79 apply (zenon_L37_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1f6 ]. % 25.56/25.79 apply (zenon_L95_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ef ]. % 25.56/25.79 apply (zenon_L97_); trivial. % 25.56/25.79 apply (zenon_L100_); trivial. % 25.56/25.79 apply (zenon_L35_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L15_); trivial. % 25.56/25.79 apply (zenon_L23_); trivial. % 25.56/25.79 (* end of lemma zenon_L101_ *) % 25.56/25.79 assert (zenon_L102_ : (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e23)) = (e20)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1f7 zenon_H84 zenon_H1f8. % 25.56/25.79 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (e20) (e20)) = (op2 (e20) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1f7. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H84. % 25.56/25.79 cut (((e20) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 25.56/25.79 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H1fa. apply refl_equal. % 25.56/25.79 apply zenon_H1f9. apply sym_equal. exact zenon_H1f8. % 25.56/25.79 (* end of lemma zenon_L102_ *) % 25.56/25.79 assert (zenon_L103_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e23)) = (e21)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H77 zenon_H4e zenon_H1fb. % 25.56/25.79 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H77. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H4e. % 25.56/25.79 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H79]. % 25.56/25.79 cut (((e21) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H63 | zenon_intro zenon_H64 ]. % 25.56/25.79 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e21) = (op2 (e20) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1fc. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H63. % 25.56/25.79 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 25.56/25.79 cut (((op2 (e20) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1fd]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H1fd zenon_H1fb). % 25.56/25.79 apply zenon_H64. apply refl_equal. % 25.56/25.79 apply zenon_H64. apply refl_equal. % 25.56/25.79 apply zenon_H79. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L103_ *) % 25.56/25.79 assert (zenon_L104_ : (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e13)) = (e10)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1fe zenon_H86 zenon_H1ff. % 25.56/25.79 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e10) (e13)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H1fe. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H86. % 25.56/25.79 cut (((e10) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 25.56/25.79 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H201. apply refl_equal. % 25.56/25.79 apply zenon_H200. apply sym_equal. exact zenon_H1ff. % 25.56/25.79 (* end of lemma zenon_L104_ *) % 25.56/25.79 assert (zenon_L105_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e13)) = (e11)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H43 zenon_H19 zenon_H202. % 25.56/25.79 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H43. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H19. % 25.56/25.79 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 25.56/25.79 cut (((e11) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H203]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H2f | zenon_intro zenon_H30 ]. % 25.56/25.79 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e11) = (op1 (e10) (e13)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H203. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H2f. % 25.56/25.79 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H30]. % 25.56/25.79 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H204]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H204 zenon_H202). % 25.56/25.79 apply zenon_H30. apply refl_equal. % 25.56/25.79 apply zenon_H30. apply refl_equal. % 25.56/25.79 apply zenon_H45. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L105_ *) % 25.56/25.79 assert (zenon_L106_ : (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((op1 (e10) (e13)) = (e13)) -> ((op2 (e20) (e23)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e13)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H205 zenon_H206 zenon_H207 zenon_H13 zenon_H14 zenon_H208. % 25.56/25.79 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H205. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H208. % 25.56/25.79 cut (((e23) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 25.56/25.79 cut (((h4 (e13)) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H20a]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [ zenon_intro zenon_H20b | zenon_intro zenon_H20c ]. % 25.56/25.79 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13)))) = ((h4 (e13)) = (h4 (op1 (e10) (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H20a. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H20b. % 25.56/25.79 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 25.56/25.79 cut (((h4 (op1 (e10) (e13))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H20e zenon_H206). % 25.56/25.79 apply zenon_H20c. apply refl_equal. % 25.56/25.79 apply zenon_H20c. apply refl_equal. % 25.56/25.79 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H20f | zenon_intro zenon_H210 ]. % 25.56/25.79 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((e23) = (op2 (h4 (e10)) (h4 (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H209. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H20f. % 25.56/25.79 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 25.56/25.79 cut (((op2 (h4 (e10)) (h4 (e13))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (h4 (e10)) (h4 (e13))) = (e23))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H211. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H207. % 25.56/25.79 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.79 cut (((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H212]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H20f | zenon_intro zenon_H210 ]. % 25.56/25.79 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H212. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H20f. % 25.56/25.79 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H210]. % 25.56/25.79 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 25.56/25.79 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.79 congruence. % 25.56/25.79 apply (zenon_L1_); trivial. % 25.56/25.79 exact (zenon_H214 zenon_H208). % 25.56/25.79 apply zenon_H210. apply refl_equal. % 25.56/25.79 apply zenon_H210. apply refl_equal. % 25.56/25.79 apply zenon_H5e. apply refl_equal. % 25.56/25.79 apply zenon_H210. apply refl_equal. % 25.56/25.79 apply zenon_H210. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L106_ *) % 25.56/25.79 assert (zenon_L107_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((op2 (e20) (e23)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e13)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H215 zenon_H86 zenon_H1fe zenon_H43 zenon_H19 zenon_H18 zenon_H2c zenon_H205 zenon_H207 zenon_H13 zenon_H14 zenon_H208. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1ff | zenon_intro zenon_H216 ]. % 25.56/25.79 apply (zenon_L104_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H216); [ zenon_intro zenon_H202 | zenon_intro zenon_H217 ]. % 25.56/25.79 apply (zenon_L105_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H217); [ zenon_intro zenon_H2d | zenon_intro zenon_H206 ]. % 25.56/25.79 apply (zenon_L7_); trivial. % 25.56/25.79 apply (zenon_L106_); trivial. % 25.56/25.79 (* end of lemma zenon_L107_ *) % 25.56/25.79 assert (zenon_L108_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e13)) = (e23)) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H80 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_H218 zenon_H1f7 zenon_H215 zenon_H1fe zenon_H205 zenon_H13 zenon_H208 zenon_H82 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H218); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H219 ]. % 25.56/25.79 apply (zenon_L102_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H219); [ zenon_intro zenon_H1fb | zenon_intro zenon_H21a ]. % 25.56/25.79 apply (zenon_L103_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H21a); [ zenon_intro zenon_H61 | zenon_intro zenon_H207 ]. % 25.56/25.79 apply (zenon_L18_); trivial. % 25.56/25.79 apply (zenon_L107_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L15_); trivial. % 25.56/25.79 apply (zenon_L23_); trivial. % 25.56/25.79 (* end of lemma zenon_L108_ *) % 25.56/25.79 assert (zenon_L109_ : (~((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 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H21b zenon_H112 zenon_Hf2 zenon_Hac zenon_H4e zenon_H13 zenon_H14. % 25.56/25.79 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H21b. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hac. % 25.56/25.79 cut (((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 25.56/25.79 cut (((h4 (e11)) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [ zenon_intro zenon_H21e | zenon_intro zenon_H21f ]. % 25.56/25.79 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10)))) = ((h4 (e11)) = (h4 (op1 (e11) (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H21d. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H21e. % 25.56/25.79 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 25.56/25.79 cut (((h4 (op1 (e11) (e10))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H116 zenon_H112). % 25.56/25.79 apply zenon_H21f. apply refl_equal. % 25.56/25.79 apply zenon_H21f. apply refl_equal. % 25.56/25.79 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H221 | zenon_intro zenon_H222 ]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H21c. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H221. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H223]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H223. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hf2. % 25.56/25.79 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 25.56/25.79 cut (((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H224]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H221 | zenon_intro zenon_H222 ]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H224. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H221. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H225]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.79 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 25.56/25.79 congruence. % 25.56/25.79 apply (zenon_L31_); trivial. % 25.56/25.79 apply (zenon_L1_); trivial. % 25.56/25.79 apply zenon_H222. apply refl_equal. % 25.56/25.79 apply zenon_H222. apply refl_equal. % 25.56/25.79 exact (zenon_H12c zenon_H4e). % 25.56/25.79 apply zenon_H222. apply refl_equal. % 25.56/25.79 apply zenon_H222. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L109_ *) % 25.56/25.79 assert (zenon_L110_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> ((op1 (e10) (e10)) = (e10)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (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) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H187 zenon_H107 zenon_H86 zenon_H14 zenon_H13 zenon_H4e zenon_Hac zenon_Hf2 zenon_H21b zenon_H17d zenon_H167 zenon_H178 zenon_H18 zenon_H118 zenon_H10c zenon_H1d zenon_H180 zenon_H183 zenon_H19. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H187); [ zenon_intro zenon_H106 | zenon_intro zenon_H18a ]. % 25.56/25.79 apply (zenon_L46_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H112 | zenon_intro zenon_H18b ]. % 25.56/25.79 apply (zenon_L109_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H18b); [ zenon_intro zenon_H117 | zenon_intro zenon_H184 ]. % 25.56/25.79 apply (zenon_L70_); trivial. % 25.56/25.79 apply (zenon_L71_); trivial. % 25.56/25.79 (* end of lemma zenon_L110_ *) % 25.56/25.79 assert (zenon_L111_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((e10) = (e11))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e22))\/((op2 (e21) (e20)) = (e23))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H82 zenon_Hb8 zenon_H1e8 zenon_Hde zenon_H100 zenon_Hfe zenon_He8 zenon_H4d zenon_H4e zenon_H187 zenon_H107 zenon_H14 zenon_H13 zenon_Hac zenon_H21b zenon_H17d zenon_H178 zenon_H118 zenon_H10c zenon_H180 zenon_H183 zenon_He2 zenon_H103 zenon_H1e2 zenon_H16d zenon_Ha7 zenon_Ha2 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.79 apply (zenon_L29_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.79 apply (zenon_L30_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hdd | zenon_intro zenon_H1e9 ]. % 25.56/25.79 apply (zenon_L38_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H167 | zenon_intro zenon_H1ea ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_He3 | zenon_intro zenon_H104 ]. % 25.56/25.79 apply (zenon_L39_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H104); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H105 ]. % 25.56/25.79 apply (zenon_L110_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H105); [ zenon_intro zenon_He9 | zenon_intro zenon_Hff ]. % 25.56/25.79 apply (zenon_L40_); trivial. % 25.56/25.79 apply (zenon_L44_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e5 ]. % 25.56/25.79 apply (zenon_L92_); trivial. % 25.56/25.79 apply (zenon_L94_); trivial. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 (* end of lemma zenon_L111_ *) % 25.56/25.79 assert (zenon_L112_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e21))\/(((op2 (e21) (e20)) = (e22))\/((op2 (e21) (e20)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e12))\/((op1 (e11) (e10)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((e10) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e11) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e11))\/((op1 (e13) (e10)) = (e11))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H80 zenon_Hba zenon_H1f4 zenon_Hd9 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_Hc0 zenon_Ha2 zenon_Ha7 zenon_H16d zenon_H1e2 zenon_H103 zenon_He2 zenon_H183 zenon_H180 zenon_H10c zenon_H118 zenon_H178 zenon_H17d zenon_H21b zenon_Hac zenon_H13 zenon_H107 zenon_H187 zenon_He8 zenon_H100 zenon_Hde zenon_H1e8 zenon_Hb8 zenon_H82 zenon_H1ec zenon_H1f2 zenon_H9c zenon_H97 zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.79 apply (zenon_L26_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1f5 ]. % 25.56/25.79 apply (zenon_L37_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1f6 ]. % 25.56/25.79 apply (zenon_L111_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ef ]. % 25.56/25.79 apply (zenon_L97_); trivial. % 25.56/25.79 apply (zenon_L100_); trivial. % 25.56/25.79 apply (zenon_L35_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L15_); trivial. % 25.56/25.79 apply (zenon_L23_); trivial. % 25.56/25.79 (* end of lemma zenon_L112_ *) % 25.56/25.79 assert (zenon_L113_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e21)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H82 zenon_Hb8 zenon_H1e8 zenon_Hde zenon_H4e zenon_Hac zenon_Hfe zenon_H208 zenon_H226 zenon_H1e2 zenon_H16d zenon_Ha7 zenon_Ha2 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.79 apply (zenon_L29_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.79 apply (zenon_L30_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hdd | zenon_intro zenon_H1e9 ]. % 25.56/25.79 apply (zenon_L38_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H167 | zenon_intro zenon_H1ea ]. % 25.56/25.79 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H226. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H208. % 25.56/25.79 cut (((e23) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 25.56/25.79 cut (((h4 (e13)) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [ zenon_intro zenon_H229 | zenon_intro zenon_H22a ]. % 25.56/25.79 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11)))) = ((h4 (e13)) = (h4 (op1 (e11) (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H228. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H229. % 25.56/25.79 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 25.56/25.79 cut (((h4 (op1 (e11) (e11))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H22b]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e11) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H22c]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H22c zenon_H167). % 25.56/25.79 apply zenon_H22a. apply refl_equal. % 25.56/25.79 apply zenon_H22a. apply refl_equal. % 25.56/25.79 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H22d | zenon_intro zenon_H22e ]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((e23) = (op2 (h4 (e11)) (h4 (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H227. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H22d. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H22e]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H22f]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e21) (e21)) = (e23)) = ((op2 (h4 (e11)) (h4 (e11))) = (e23))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H22f. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hfe. % 25.56/25.79 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.79 cut (((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H230]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H22d | zenon_intro zenon_H22e ]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H230. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H22d. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H22e]. % 25.56/25.79 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H231]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 25.56/25.79 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 25.56/25.79 congruence. % 25.56/25.79 apply (zenon_L31_); trivial. % 25.56/25.79 apply (zenon_L31_); trivial. % 25.56/25.79 apply zenon_H22e. apply refl_equal. % 25.56/25.79 apply zenon_H22e. apply refl_equal. % 25.56/25.79 apply zenon_H5e. apply refl_equal. % 25.56/25.79 apply zenon_H22e. apply refl_equal. % 25.56/25.79 apply zenon_H22e. apply refl_equal. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e5 ]. % 25.56/25.79 apply (zenon_L92_); trivial. % 25.56/25.79 apply (zenon_L94_); trivial. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 (* end of lemma zenon_L113_ *) % 25.56/25.79 assert (zenon_L114_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H189 zenon_H10c zenon_H1c zenon_Hac zenon_Hbe zenon_H13 zenon_H232 zenon_H1d zenon_H18 zenon_H19 zenon_H174. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H10d | zenon_intro zenon_H18c ]. % 25.56/25.79 apply (zenon_L47_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H1e | zenon_intro zenon_H18d ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H147 | zenon_intro zenon_H173 ]. % 25.56/25.79 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H232. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H13. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H233]. % 25.56/25.79 cut (((h4 (e10)) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H234]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [ zenon_intro zenon_H235 | zenon_intro zenon_H236 ]. % 25.56/25.79 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12)))) = ((h4 (e10)) = (h4 (op1 (e11) (e12))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H234. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H235. % 25.56/25.79 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H236]. % 25.56/25.79 cut (((h4 (op1 (e11) (e12))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H237]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e11) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H238 zenon_H147). % 25.56/25.79 apply zenon_H236. apply refl_equal. % 25.56/25.79 apply zenon_H236. apply refl_equal. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (e23)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H239]. % 25.56/25.79 cut (((op2 (e23) (e23)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H23a. apply sym_equal. exact zenon_Hac. % 25.56/25.79 apply zenon_H239. apply sym_equal. exact zenon_Hbe. % 25.56/25.79 apply (zenon_L67_); trivial. % 25.56/25.79 (* end of lemma zenon_L114_ *) % 25.56/25.79 assert (zenon_L115_ : (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op1 (e11) (e13)) = (e12)) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H23b zenon_Hbe zenon_H35 zenon_H208 zenon_Hac. % 25.56/25.79 cut (((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H23b. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hbe. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 25.56/25.79 cut (((h4 (e12)) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [ zenon_intro zenon_H23e | zenon_intro zenon_H23f ]. % 25.56/25.79 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13)))) = ((h4 (e12)) = (h4 (op1 (e11) (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H23d. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H23e. % 25.56/25.79 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H23f]. % 25.56/25.79 cut (((h4 (op1 (e11) (e13))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H3a zenon_H35). % 25.56/25.79 apply zenon_H23f. apply refl_equal. % 25.56/25.79 apply zenon_H23f. apply refl_equal. % 25.56/25.79 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 25.56/25.79 cut (((op2 (e23) (e23)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H23a]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H23a. apply sym_equal. exact zenon_Hac. % 25.56/25.79 apply zenon_H241. apply sym_equal. exact zenon_H208. % 25.56/25.79 (* end of lemma zenon_L115_ *) % 25.56/25.79 assert (zenon_L116_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H49 zenon_H2c zenon_Hac zenon_H208 zenon_Hbe zenon_H23b zenon_H16d zenon_H18 zenon_H19 zenon_Hb8. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H2d | zenon_intro zenon_H4a ]. % 25.56/25.79 apply (zenon_L7_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H35 | zenon_intro zenon_H4b ]. % 25.56/25.79 apply (zenon_L115_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H3b | zenon_intro zenon_H42 ]. % 25.56/25.79 apply (zenon_L65_); trivial. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 (* end of lemma zenon_L116_ *) % 25.56/25.79 assert (zenon_L117_ : (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((op1 (e13) (e12)) = (e12)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H242 zenon_Hae zenon_H243. % 25.56/25.79 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e13) (e12)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H242. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hae. % 25.56/25.79 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 25.56/25.79 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H26. apply refl_equal. % 25.56/25.79 apply zenon_H244. apply sym_equal. exact zenon_H243. % 25.56/25.79 (* end of lemma zenon_L117_ *) % 25.56/25.79 assert (zenon_L118_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H245 zenon_H246 zenon_H247. % 25.56/25.79 cut (((op1 (e13) (e10)) = (e13)) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H245. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H246. % 25.56/25.79 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H248]. % 25.56/25.79 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H14f. apply refl_equal. % 25.56/25.79 apply zenon_H248. apply sym_equal. exact zenon_H247. % 25.56/25.79 (* end of lemma zenon_L118_ *) % 25.56/25.79 assert (zenon_L119_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e13)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H249 zenon_H15d zenon_H18 zenon_H1d zenon_H19 zenon_H137 zenon_Hae zenon_H242 zenon_H245 zenon_H246. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H15c | zenon_intro zenon_H24a ]. % 25.56/25.79 apply (zenon_L60_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H138 | zenon_intro zenon_H24b ]. % 25.56/25.79 apply (zenon_L54_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H24b); [ zenon_intro zenon_H243 | zenon_intro zenon_H247 ]. % 25.56/25.79 apply (zenon_L117_); trivial. % 25.56/25.79 apply (zenon_L118_); trivial. % 25.56/25.79 (* end of lemma zenon_L119_ *) % 25.56/25.79 assert (zenon_L120_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((e10) = (e13))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e22) (e20)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H24c zenon_Hde zenon_H86 zenon_H17d zenon_H167 zenon_H14 zenon_H13 zenon_H4d zenon_Hbe zenon_H24d zenon_H208 zenon_H24e zenon_H249 zenon_H15d zenon_H18 zenon_H1d zenon_H19 zenon_H137 zenon_Hae zenon_H242 zenon_H245. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_Hdd | zenon_intro zenon_H24f ]. % 25.56/25.79 apply (zenon_L38_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H17c | zenon_intro zenon_H250 ]. % 25.56/25.79 apply (zenon_L69_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H250); [ zenon_intro zenon_H251 | zenon_intro zenon_H246 ]. % 25.56/25.79 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H24e. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H208. % 25.56/25.79 cut (((e23) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H252]. % 25.56/25.79 cut (((h4 (e13)) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [ zenon_intro zenon_H254 | zenon_intro zenon_H255 ]. % 25.56/25.79 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10)))) = ((h4 (e13)) = (h4 (op1 (e12) (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H253. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H254. % 25.56/25.79 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H255]. % 25.56/25.79 cut (((h4 (op1 (e12) (e10))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H256]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H257]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H257 zenon_H251). % 25.56/25.79 apply zenon_H255. apply refl_equal. % 25.56/25.79 apply zenon_H255. apply refl_equal. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H258 | zenon_intro zenon_H259 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((e23) = (op2 (h4 (e12)) (h4 (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H252. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H258. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e10))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e22) (e20)) = (e23)) = ((op2 (h4 (e12)) (h4 (e10))) = (e23))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H25a. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H24d. % 25.56/25.79 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.79 cut (((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H258 | zenon_intro zenon_H259 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H25b. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H258. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.79 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 25.56/25.79 congruence. % 25.56/25.79 apply (zenon_L50_); trivial. % 25.56/25.79 apply (zenon_L1_); trivial. % 25.56/25.79 apply zenon_H259. apply refl_equal. % 25.56/25.79 apply zenon_H259. apply refl_equal. % 25.56/25.79 apply zenon_H5e. apply refl_equal. % 25.56/25.79 apply zenon_H259. apply refl_equal. % 25.56/25.79 apply zenon_H259. apply refl_equal. % 25.56/25.79 apply (zenon_L119_); trivial. % 25.56/25.79 (* end of lemma zenon_L120_ *) % 25.56/25.79 assert (zenon_L121_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e23) (e22)) = (e20)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H14 zenon_H25d zenon_H4d zenon_H4e zenon_H25e. % 25.56/25.79 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 25.56/25.79 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((op2 (e21) (e22)) = (op2 (e23) (e22)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H25e. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H19f. % 25.56/25.79 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 25.56/25.79 cut (((op2 (e23) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H25f]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e23) (e22)) = (op2 (e21) (e22)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H25f. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H14. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 25.56/25.79 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H260]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H19f | zenon_intro zenon_H1a0 ]. % 25.56/25.79 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e20) = (op2 (e23) (e22)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H260. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H19f. % 25.56/25.79 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1a0]. % 25.56/25.79 cut (((op2 (e23) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H261 zenon_H25d). % 25.56/25.79 apply zenon_H1a0. apply refl_equal. % 25.56/25.79 apply zenon_H1a0. apply refl_equal. % 25.56/25.79 apply (zenon_L13_); trivial. % 25.56/25.79 apply zenon_H1a0. apply refl_equal. % 25.56/25.79 apply zenon_H1a0. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L121_ *) % 25.56/25.79 assert (zenon_L122_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e23) (e22)) = (e22)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H262 zenon_Hb3 zenon_H263. % 25.56/25.79 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H262. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hb3. % 25.56/25.79 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 25.56/25.79 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H5a. apply refl_equal. % 25.56/25.79 apply zenon_H264. apply sym_equal. exact zenon_H263. % 25.56/25.79 (* end of lemma zenon_L122_ *) % 25.56/25.79 assert (zenon_L123_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H265 zenon_H266 zenon_H267. % 25.56/25.79 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H265. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H266. % 25.56/25.79 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 25.56/25.79 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 25.56/25.79 congruence. % 25.56/25.79 apply zenon_H269. apply refl_equal. % 25.56/25.79 apply zenon_H268. apply sym_equal. exact zenon_H267. % 25.56/25.79 (* end of lemma zenon_L123_ *) % 25.56/25.79 assert (zenon_L124_ : (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H26a zenon_H25e zenon_H4d zenon_H14 zenon_H4e zenon_H19c zenon_Hb3 zenon_H262 zenon_H265 zenon_H266. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H25d | zenon_intro zenon_H26b ]. % 25.56/25.79 apply (zenon_L121_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H19d | zenon_intro zenon_H26c ]. % 25.56/25.79 apply (zenon_L76_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H263 | zenon_intro zenon_H267 ]. % 25.56/25.79 apply (zenon_L122_); trivial. % 25.56/25.79 apply (zenon_L123_); trivial. % 25.56/25.79 (* end of lemma zenon_L124_ *) % 25.56/25.79 assert (zenon_L125_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e20)) = (e23))\/(((op2 (e22) (e20)) = (e23))\/((op2 (e23) (e20)) = (e23))))) -> (~((e20) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (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))))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H80 zenon_Hba zenon_H1f4 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_Hc0 zenon_Ha2 zenon_Ha7 zenon_H16d zenon_H1e2 zenon_H26d zenon_Hd9 zenon_H100 zenon_H245 zenon_H242 zenon_H137 zenon_H15d zenon_H249 zenon_H24e zenon_H208 zenon_Hbe zenon_H13 zenon_H17d zenon_Hde zenon_H24c zenon_H26a zenon_H25e zenon_H19c zenon_H262 zenon_H265 zenon_H1e8 zenon_Hb8 zenon_H82 zenon_H1ec zenon_H1f2 zenon_H9c zenon_H97 zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.79 apply (zenon_L26_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1f5 ]. % 25.56/25.79 apply (zenon_L37_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1f6 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.79 apply (zenon_L29_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.79 apply (zenon_L30_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hdd | zenon_intro zenon_H1e9 ]. % 25.56/25.79 apply (zenon_L38_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H167 | zenon_intro zenon_H1ea ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H26d); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H26e ]. % 25.56/25.79 apply (zenon_L37_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H26e); [ zenon_intro zenon_Hff | zenon_intro zenon_H26f ]. % 25.56/25.79 apply (zenon_L44_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H26f); [ zenon_intro zenon_H24d | zenon_intro zenon_H266 ]. % 25.56/25.79 apply (zenon_L120_); trivial. % 25.56/25.79 apply (zenon_L124_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e5 ]. % 25.56/25.79 apply (zenon_L92_); trivial. % 25.56/25.79 apply (zenon_L94_); trivial. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ef ]. % 25.56/25.79 apply (zenon_L97_); trivial. % 25.56/25.79 apply (zenon_L100_); trivial. % 25.56/25.79 apply (zenon_L35_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L15_); trivial. % 25.56/25.79 apply (zenon_L23_); trivial. % 25.56/25.79 (* end of lemma zenon_L125_ *) % 25.56/25.79 assert (zenon_L126_ : ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H195 zenon_Hbe zenon_H4d zenon_Hac zenon_H4e zenon_H270. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H271 | zenon_intro zenon_H272 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H270. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H271. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H273]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e22) (e21)) = (e21)) = ((op2 (h4 (e12)) (h4 (e11))) = (op2 (e23) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H273. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H195. % 25.56/25.79 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H12c]. % 25.56/25.79 cut (((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H274]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H271 | zenon_intro zenon_H272 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H274. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H271. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 25.56/25.79 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 25.56/25.79 congruence. % 25.56/25.79 apply (zenon_L50_); trivial. % 25.56/25.79 apply (zenon_L31_); trivial. % 25.56/25.79 apply zenon_H272. apply refl_equal. % 25.56/25.79 apply zenon_H272. apply refl_equal. % 25.56/25.79 exact (zenon_H12c zenon_H4e). % 25.56/25.79 apply zenon_H272. apply refl_equal. % 25.56/25.79 apply zenon_H272. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L126_ *) % 25.56/25.79 assert (zenon_L127_ : (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((op1 (e12) (e11)) = (e11)) -> ((op2 (e22) (e21)) = (e21)) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H276 zenon_H130 zenon_H195 zenon_Hbe zenon_H4d zenon_Hac zenon_H4e. % 25.56/25.79 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H276. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hac. % 25.56/25.79 cut (((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 25.56/25.79 cut (((h4 (e11)) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H277]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H278 | zenon_intro zenon_H279 ]. % 25.56/25.79 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((h4 (e11)) = (h4 (op1 (e12) (e11))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H277. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H278. % 25.56/25.79 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 25.56/25.79 cut (((h4 (op1 (e12) (e11))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e12) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H27b zenon_H130). % 25.56/25.79 apply zenon_H279. apply refl_equal. % 25.56/25.79 apply zenon_H279. apply refl_equal. % 25.56/25.79 apply (zenon_L126_); trivial. % 25.56/25.79 (* end of lemma zenon_L127_ *) % 25.56/25.79 assert (zenon_L128_ : (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e10)) -> ((op1 (e11) (e12)) = (e10)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H16a zenon_H18 zenon_H19 zenon_H154 zenon_H147 zenon_H1d zenon_H156 zenon_H4e zenon_Hac zenon_H4d zenon_Hbe zenon_H195 zenon_H276 zenon_H133 zenon_Hae zenon_H166 zenon_H167. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H16a); [ zenon_intro zenon_H157 | zenon_intro zenon_H16b ]. % 25.56/25.79 apply (zenon_L59_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H16b); [ zenon_intro zenon_H130 | zenon_intro zenon_H16c ]. % 25.56/25.79 apply (zenon_L127_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H16c); [ zenon_intro zenon_H164 | zenon_intro zenon_H168 ]. % 25.56/25.79 apply (zenon_L62_); trivial. % 25.56/25.79 apply (zenon_L63_); trivial. % 25.56/25.79 (* end of lemma zenon_L128_ *) % 25.56/25.79 assert (zenon_L129_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (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 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H189 zenon_H10c zenon_H1c zenon_H43 zenon_H3c zenon_H2c zenon_H49 zenon_H15d zenon_H16a zenon_H156 zenon_H4e zenon_Hac zenon_H4d zenon_Hbe zenon_H195 zenon_H276 zenon_H133 zenon_Hae zenon_H166 zenon_H167 zenon_H86 zenon_H14d zenon_H161 zenon_H1d zenon_H18 zenon_H19 zenon_H174. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H10d | zenon_intro zenon_H18c ]. % 25.56/25.79 apply (zenon_L47_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H1e | zenon_intro zenon_H18d ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H147 | zenon_intro zenon_H173 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H14c | zenon_intro zenon_H162 ]. % 25.56/25.79 apply (zenon_L57_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H154 | zenon_intro zenon_H163 ]. % 25.56/25.79 apply (zenon_L128_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H15c | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L60_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 apply (zenon_L67_); trivial. % 25.56/25.79 (* end of lemma zenon_L129_ *) % 25.56/25.79 assert (zenon_L130_ : (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> ((op2 (e23) (e21)) = (e20)) -> ((op2 (e21) (e22)) = (e20)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> ((op1 (e10) (e10)) = (e10)) -> ((op1 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (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 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e21)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H1cd zenon_H1a7 zenon_H1a6 zenon_H14 zenon_H1ac zenon_H174 zenon_H19 zenon_H18 zenon_H1d zenon_H161 zenon_H14d zenon_H86 zenon_H167 zenon_H166 zenon_Hae zenon_H133 zenon_H276 zenon_Hbe zenon_H4d zenon_Hac zenon_H4e zenon_H156 zenon_H16a zenon_H15d zenon_H49 zenon_H2c zenon_H3c zenon_H43 zenon_H1c zenon_H10c zenon_H189 zenon_H198 zenon_Hb3 zenon_H1ca zenon_Hfe. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H1ad | zenon_intro zenon_H1ce ]. % 25.56/25.79 apply (zenon_L79_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1ce); [ zenon_intro zenon_H195 | zenon_intro zenon_H1cf ]. % 25.56/25.79 apply (zenon_L129_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1cf); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H1cb ]. % 25.56/25.79 apply (zenon_L85_); trivial. % 25.56/25.79 apply (zenon_L86_); trivial. % 25.56/25.79 (* end of lemma zenon_L130_ *) % 25.56/25.79 assert (zenon_L131_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e10) = (e13))) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e21)) = (e23)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((e20) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H82 zenon_Hb8 zenon_H1e8 zenon_Hde zenon_H4e zenon_H4d zenon_H60 zenon_Hb3 zenon_Hb5 zenon_H1da zenon_He2 zenon_H51 zenon_Hfe zenon_H1c2 zenon_H1be zenon_H1b2 zenon_H1cd zenon_H1ac zenon_H174 zenon_H161 zenon_H14d zenon_H166 zenon_H133 zenon_H276 zenon_Hbe zenon_Hac zenon_H156 zenon_H16a zenon_H15d zenon_H10c zenon_H189 zenon_H198 zenon_H1ca zenon_H1c5 zenon_H9c zenon_He8 zenon_H1d8 zenon_H14 zenon_Hec zenon_H84 zenon_H97 zenon_Hbc zenon_H1e2 zenon_H16d zenon_Ha7 zenon_Ha2 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.79 apply (zenon_L29_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.79 apply (zenon_L30_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hdd | zenon_intro zenon_H1e9 ]. % 25.56/25.79 apply (zenon_L38_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H167 | zenon_intro zenon_H1ea ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc6 ]. % 25.56/25.79 apply (zenon_L26_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_He3 | zenon_intro zenon_H1db ]. % 25.56/25.79 apply (zenon_L39_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H52 | zenon_intro zenon_H1dc ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1d4 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_He9 | zenon_intro zenon_H1dd ]. % 25.56/25.79 apply (zenon_L40_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hed | zenon_intro zenon_H69 ]. % 25.56/25.79 apply (zenon_L41_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H1c6 ]. % 25.56/25.79 apply (zenon_L130_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1b3 | zenon_intro zenon_H1c7 ]. % 25.56/25.79 apply (zenon_L80_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1c7); [ zenon_intro zenon_H1bd | zenon_intro zenon_H1c3 ]. % 25.56/25.79 apply (zenon_L82_); trivial. % 25.56/25.79 apply (zenon_L83_); trivial. % 25.56/25.79 apply (zenon_L89_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H61 ]. % 25.56/25.79 apply (zenon_L33_); trivial. % 25.56/25.79 apply (zenon_L18_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e5 ]. % 25.56/25.79 apply (zenon_L92_); trivial. % 25.56/25.79 apply (zenon_L94_); trivial. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 (* end of lemma zenon_L131_ *) % 25.56/25.79 assert (zenon_L132_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e22) (e22)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e12) = (e13))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e21)) = (e22))\/((op2 (e23) (e21)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((e10) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((e22) = (e23))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H80 zenon_Hba zenon_H1f4 zenon_Hd9 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_Hc0 zenon_Ha2 zenon_Ha7 zenon_H16d zenon_H1e2 zenon_Hbc zenon_H97 zenon_Hec zenon_H1d8 zenon_He8 zenon_H9c zenon_H1c5 zenon_H1ca zenon_H198 zenon_H189 zenon_H10c zenon_H15d zenon_H16a zenon_H156 zenon_Hac zenon_Hbe zenon_H276 zenon_H133 zenon_H166 zenon_H14d zenon_H161 zenon_H174 zenon_H1ac zenon_H1cd zenon_H1b2 zenon_H1be zenon_H1c2 zenon_He2 zenon_H1da zenon_Hb5 zenon_Hde zenon_H1e8 zenon_Hb8 zenon_H82 zenon_H1ec zenon_H1f2 zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.79 apply (zenon_L26_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1f5 ]. % 25.56/25.79 apply (zenon_L37_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1f6 ]. % 25.56/25.79 apply (zenon_L131_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ef ]. % 25.56/25.79 apply (zenon_L97_); trivial. % 25.56/25.79 apply (zenon_L100_); trivial. % 25.56/25.79 apply (zenon_L35_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L15_); trivial. % 25.56/25.79 apply (zenon_L23_); trivial. % 25.56/25.79 (* end of lemma zenon_L132_ *) % 25.56/25.79 assert (zenon_L133_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H80 zenon_Hba zenon_H82 zenon_Hb8 zenon_H27c zenon_Hbe zenon_Ha7 zenon_Ha2 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43 zenon_H9c zenon_H97 zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.79 apply (zenon_L26_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.79 apply (zenon_L29_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.79 apply (zenon_L30_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.79 cut (((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H27c. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hbe. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H27d]. % 25.56/25.79 cut (((h4 (e12)) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [ zenon_intro zenon_H27f | zenon_intro zenon_H280 ]. % 25.56/25.79 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12)))) = ((h4 (e12)) = (h4 (op1 (e12) (e12))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H27e. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H27f. % 25.56/25.79 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 25.56/25.79 cut (((h4 (op1 (e12) (e12))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e12) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H282]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H282 zenon_Hae). % 25.56/25.79 apply zenon_H280. apply refl_equal. % 25.56/25.79 apply zenon_H280. apply refl_equal. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H283 | zenon_intro zenon_H284 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (op2 (e23) (e23)) (e23)) = (op2 (h4 (e12)) (h4 (e12))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H27d. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H283. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H285]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (h4 (e12)) (h4 (e12))) = (op2 (op2 (e23) (e23)) (e23)))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H285. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hb3. % 25.56/25.79 cut (((e22) = (op2 (op2 (e23) (e23)) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 25.56/25.79 cut (((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H283 | zenon_intro zenon_H284 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H286. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H283. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 25.56/25.79 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 25.56/25.79 congruence. % 25.56/25.79 apply (zenon_L50_); trivial. % 25.56/25.79 apply (zenon_L50_); trivial. % 25.56/25.79 apply zenon_H284. apply refl_equal. % 25.56/25.79 apply zenon_H284. apply refl_equal. % 25.56/25.79 exact (zenon_Hd5 zenon_H4d). % 25.56/25.79 apply zenon_H284. apply refl_equal. % 25.56/25.79 apply zenon_H284. apply refl_equal. % 25.56/25.79 apply (zenon_L34_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 apply (zenon_L35_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L15_); trivial. % 25.56/25.79 apply (zenon_L23_); trivial. % 25.56/25.79 (* end of lemma zenon_L133_ *) % 25.56/25.79 assert (zenon_L134_ : (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 25.56/25.79 do 0 intro. intros zenon_H288 zenon_H13 zenon_H289 zenon_H28a zenon_H14 zenon_Hbe zenon_H4d zenon_H208. % 25.56/25.79 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H288. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H13. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H28b]. % 25.56/25.79 cut (((h4 (e10)) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [ zenon_intro zenon_H28d | zenon_intro zenon_H28e ]. % 25.56/25.79 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13)))) = ((h4 (e10)) = (h4 (op1 (e12) (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H28c. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H28d. % 25.56/25.79 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 25.56/25.79 cut (((h4 (op1 (e12) (e13))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H28f]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H290]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H290 zenon_H289). % 25.56/25.79 apply zenon_H28e. apply refl_equal. % 25.56/25.79 apply zenon_H28e. apply refl_equal. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H291 | zenon_intro zenon_H292 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (h4 (e12)) (h4 (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H28b. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H291. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H293]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e22) (e23)) = (e20)) = ((op2 (h4 (e12)) (h4 (e13))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H293. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H28a. % 25.56/25.79 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 25.56/25.79 cut (((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H291 | zenon_intro zenon_H292 ]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H294. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H291. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 25.56/25.79 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 25.56/25.79 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 25.56/25.79 congruence. % 25.56/25.79 apply (zenon_L50_); trivial. % 25.56/25.79 exact (zenon_H214 zenon_H208). % 25.56/25.79 apply zenon_H292. apply refl_equal. % 25.56/25.79 apply zenon_H292. apply refl_equal. % 25.56/25.79 exact (zenon_H90 zenon_H14). % 25.56/25.79 apply zenon_H292. apply refl_equal. % 25.56/25.79 apply zenon_H292. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L134_ *) % 25.56/25.79 assert (zenon_L135_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (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))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H296 zenon_H86 zenon_H1fe zenon_H174 zenon_H1d zenon_H208 zenon_H4d zenon_Hbe zenon_H14 zenon_H28a zenon_H13 zenon_H288 zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H296); [ zenon_intro zenon_H1ff | zenon_intro zenon_H297 ]. % 25.56/25.79 apply (zenon_L104_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_H173 | zenon_intro zenon_H298 ]. % 25.56/25.79 apply (zenon_L67_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H289 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L134_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 (* end of lemma zenon_L135_ *) % 25.56/25.79 assert (zenon_L136_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e13)) = (e23)) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H80 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_H1d8 zenon_He8 zenon_H9c zenon_H299 zenon_H1f7 zenon_Hec zenon_H288 zenon_H13 zenon_Hbe zenon_H208 zenon_H174 zenon_H1fe zenon_H296 zenon_H82 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_He9 | zenon_intro zenon_H1dd ]. % 25.56/25.79 apply (zenon_L40_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 25.56/25.79 apply (zenon_L27_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hed | zenon_intro zenon_H69 ]. % 25.56/25.79 apply (zenon_L41_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_H1f8 | zenon_intro zenon_H29a ]. % 25.56/25.79 apply (zenon_L102_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H29a); [ zenon_intro zenon_H1d4 | zenon_intro zenon_H29b ]. % 25.56/25.79 apply (zenon_L89_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H29b); [ zenon_intro zenon_H28a | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L135_); trivial. % 25.56/25.79 apply (zenon_L20_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.79 apply (zenon_L3_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.79 apply (zenon_L4_); trivial. % 25.56/25.79 apply (zenon_L12_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.79 apply (zenon_L14_); trivial. % 25.56/25.79 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.79 apply (zenon_L15_); trivial. % 25.56/25.79 apply (zenon_L23_); trivial. % 25.56/25.79 (* end of lemma zenon_L136_ *) % 25.56/25.79 assert (zenon_L137_ : ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op1 (e13) (e10)) = (e12)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((e22) = (h4 (op1 (e13) (e10))))) -> False). % 25.56/25.79 do 0 intro. intros zenon_Hbe zenon_H29c zenon_H4d zenon_H29d. % 25.56/25.79 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H29e | zenon_intro zenon_H29f ]. % 25.56/25.79 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((e22) = (h4 (op1 (e13) (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H29d. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H29e. % 25.56/25.79 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H29f]. % 25.56/25.79 cut (((h4 (op1 (e13) (e10))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H2a0]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) = ((h4 (op1 (e13) (e10))) = (e22))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H2a0. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_Hbe. % 25.56/25.79 cut (((op2 (op2 (e23) (e23)) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H4f]. % 25.56/25.79 cut (((h4 (e12)) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H2a1]. % 25.56/25.79 congruence. % 25.56/25.79 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H29e | zenon_intro zenon_H29f ]. % 25.56/25.79 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((h4 (e12)) = (h4 (op1 (e13) (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H2a1. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H29e. % 25.56/25.79 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H29f]. % 25.56/25.79 cut (((h4 (op1 (e13) (e10))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2a3]. % 25.56/25.79 congruence. % 25.56/25.79 exact (zenon_H2a3 zenon_H29c). % 25.56/25.79 apply zenon_H29f. apply refl_equal. % 25.56/25.79 apply zenon_H29f. apply refl_equal. % 25.56/25.79 apply zenon_H4f. apply sym_equal. exact zenon_H4d. % 25.56/25.79 apply zenon_H29f. apply refl_equal. % 25.56/25.79 apply zenon_H29f. apply refl_equal. % 25.56/25.79 (* end of lemma zenon_L137_ *) % 25.56/25.79 assert (zenon_L138_ : ((op2 (e23) (e20)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op1 (e13) (e10)) = (e12)) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> False). % 25.56/25.79 do 0 intro. intros zenon_H2a4 zenon_H208 zenon_H13 zenon_H14 zenon_Hbe zenon_H4d zenon_H29c zenon_H2a5. % 25.56/25.79 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H2a6 | zenon_intro zenon_H2a7 ]. % 25.56/25.79 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H2a5. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H2a6. % 25.56/25.79 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 25.56/25.79 cut (((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H2a8]. % 25.56/25.79 congruence. % 25.56/25.79 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))). % 25.56/25.79 intro zenon_D_pnotp. % 25.56/25.79 apply zenon_H2a8. % 25.56/25.79 rewrite <- zenon_D_pnotp. % 25.56/25.79 exact zenon_H2a4. % 25.56/25.79 cut (((e22) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H29d]. % 25.56/25.79 cut (((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H2a9]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H2a6 | zenon_intro zenon_H2a7 ]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2a9. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2a6. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H2a7]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2aa]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 25.56/25.80 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 25.56/25.80 congruence. % 25.56/25.80 exact (zenon_H214 zenon_H208). % 25.56/25.80 apply (zenon_L1_); trivial. % 25.56/25.80 apply zenon_H2a7. apply refl_equal. % 25.56/25.80 apply zenon_H2a7. apply refl_equal. % 25.56/25.80 apply (zenon_L137_); trivial. % 25.56/25.80 apply zenon_H2a7. apply refl_equal. % 25.56/25.80 apply zenon_H2a7. apply refl_equal. % 25.56/25.80 (* end of lemma zenon_L138_ *) % 25.56/25.80 assert (zenon_L139_ : (~((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e11)))) -> ((op1 (e11) (e13)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e11)) = (e12)) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2ab zenon_H35 zenon_H19 zenon_Hcb. % 25.56/25.80 cut (((op1 (e11) (e13)) = (e12)) = ((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e11)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2ab. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H35. % 25.56/25.80 cut (((e12) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2ac]. % 25.56/25.80 cut (((op1 (e11) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2ad]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [ zenon_intro zenon_H2ae | zenon_intro zenon_H2af ]. % 25.56/25.80 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e11) (e13)) = (op1 (op1 (e13) (e13)) (e13)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2ad. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2ae. % 25.56/25.80 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (op1 (e13) (e13)) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2af]. % 25.56/25.80 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 25.56/25.80 congruence. % 25.56/25.80 apply (zenon_L6_); trivial. % 25.56/25.80 apply zenon_H2af. apply refl_equal. % 25.56/25.80 apply zenon_H2af. apply refl_equal. % 25.56/25.80 apply zenon_H2ac. apply sym_equal. exact zenon_Hcb. % 25.56/25.80 (* end of lemma zenon_L139_ *) % 25.56/25.80 assert (zenon_L140_ : ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e13) (e11)) = (e12)) -> ((op1 (e11) (e13)) = (e12)) -> ((op1 (e10) (e11)) = (e12)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H18 zenon_H2b0 zenon_H35 zenon_Hcb zenon_H19 zenon_H2b1. % 25.56/25.80 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b3 ]. % 25.56/25.80 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e10) (e11)) = (op1 (e13) (e11)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2b1. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2b2. % 25.56/25.80 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 25.56/25.80 cut (((op1 (e13) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((e12) = (op1 (op1 (e13) (e13)) (e13))) = ((op1 (e13) (e11)) = (op1 (e10) (e11)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2b4. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H18. % 25.56/25.80 cut (((op1 (op1 (e13) (e13)) (e13)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2ab]. % 25.56/25.80 cut (((e12) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_H2b2 | zenon_intro zenon_H2b3 ]. % 25.56/25.80 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e12) = (op1 (e13) (e11)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2b5. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2b2. % 25.56/25.80 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2b3]. % 25.56/25.80 cut (((op1 (e13) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2b6]. % 25.56/25.80 congruence. % 25.56/25.80 exact (zenon_H2b6 zenon_H2b0). % 25.56/25.80 apply zenon_H2b3. apply refl_equal. % 25.56/25.80 apply zenon_H2b3. apply refl_equal. % 25.56/25.80 apply (zenon_L139_); trivial. % 25.56/25.80 apply zenon_H2b3. apply refl_equal. % 25.56/25.80 apply zenon_H2b3. apply refl_equal. % 25.56/25.80 (* end of lemma zenon_L140_ *) % 25.56/25.80 assert (zenon_L141_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((e10) = (e12))) -> ((op1 (e10) (e10)) = (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 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((op2 (e23) (e20)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 25.56/25.80 do 0 intro. intros zenon_Hbf zenon_Ha2 zenon_H86 zenon_Hb8 zenon_H242 zenon_H49 zenon_H2b1 zenon_H16d zenon_H2a4 zenon_H208 zenon_H13 zenon_H14 zenon_Hbe zenon_H4d zenon_H2a5 zenon_H2b7 zenon_Hb0 zenon_Hae zenon_H2c zenon_H18 zenon_H19. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hbf); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc9 ]. % 25.56/25.80 apply (zenon_L29_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc9); [ zenon_intro zenon_Hcb | zenon_intro zenon_Hca ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2b7); [ zenon_intro zenon_H29c | zenon_intro zenon_H2b8 ]. % 25.56/25.80 apply (zenon_L138_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H2b0 | zenon_intro zenon_H2b9 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H2d | zenon_intro zenon_H4a ]. % 25.56/25.80 apply (zenon_L7_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H35 | zenon_intro zenon_H4b ]. % 25.56/25.80 apply (zenon_L140_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H3b | zenon_intro zenon_H42 ]. % 25.56/25.80 apply (zenon_L65_); trivial. % 25.56/25.80 apply (zenon_L34_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2b9); [ zenon_intro zenon_H243 | zenon_intro zenon_H42 ]. % 25.56/25.80 apply (zenon_L117_); trivial. % 25.56/25.80 apply (zenon_L34_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Haf | zenon_intro zenon_H2d ]. % 25.56/25.80 apply (zenon_L32_); trivial. % 25.56/25.80 apply (zenon_L7_); trivial. % 25.56/25.80 (* end of lemma zenon_L141_ *) % 25.56/25.80 assert (zenon_L142_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((e20) = (e22))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e23) (e21)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op2 (e23) (e20)) = (e22))\/(((op2 (e23) (e21)) = (e22))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H80 zenon_Hba zenon_H82 zenon_Hb8 zenon_Hbc zenon_H97 zenon_H262 zenon_H1be zenon_Hbf zenon_Ha2 zenon_H242 zenon_H2b1 zenon_H16d zenon_H208 zenon_H13 zenon_Hbe zenon_H2a5 zenon_H2b7 zenon_Hb0 zenon_H2ba zenon_Hec zenon_H9c zenon_He8 zenon_H1d8 zenon_Hb5 zenon_Ha7 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43 zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.80 apply (zenon_L26_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.80 apply (zenon_L27_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.80 apply (zenon_L29_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.80 apply (zenon_L30_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hbc); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc6 ]. % 25.56/25.80 apply (zenon_L26_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc6); [ zenon_intro zenon_Hc8 | zenon_intro zenon_Hc7 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_He9 | zenon_intro zenon_H1dd ]. % 25.56/25.80 apply (zenon_L40_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 25.56/25.80 apply (zenon_L27_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hed | zenon_intro zenon_H69 ]. % 25.56/25.80 apply (zenon_L41_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H2a4 | zenon_intro zenon_H2bb ]. % 25.56/25.80 apply (zenon_L141_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_H1bd | zenon_intro zenon_H2bc ]. % 25.56/25.80 apply (zenon_L82_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2bc); [ zenon_intro zenon_H263 | zenon_intro zenon_H76 ]. % 25.56/25.80 apply (zenon_L122_); trivial. % 25.56/25.80 apply (zenon_L35_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc7); [ zenon_intro zenon_Hb4 | zenon_intro zenon_H61 ]. % 25.56/25.80 apply (zenon_L33_); trivial. % 25.56/25.80 apply (zenon_L18_); trivial. % 25.56/25.80 apply (zenon_L34_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.80 apply (zenon_L3_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.80 apply (zenon_L4_); trivial. % 25.56/25.80 apply (zenon_L12_); trivial. % 25.56/25.80 apply (zenon_L35_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.80 apply (zenon_L14_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.80 apply (zenon_L15_); trivial. % 25.56/25.80 apply (zenon_L23_); trivial. % 25.56/25.80 (* end of lemma zenon_L142_ *) % 25.56/25.80 assert (zenon_L143_ : (~((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e20) (e20)))) -> ((op2 (e21) (e22)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e20) (e20)) = (e20)) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2bd zenon_H1a6 zenon_H4e zenon_H4d zenon_H84. % 25.56/25.80 cut (((op2 (e21) (e22)) = (e20)) = ((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e20) (e20)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2bd. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H1a6. % 25.56/25.80 cut (((e20) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2be]. % 25.56/25.80 cut (((op2 (e21) (e22)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1a9]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1ab ]. % 25.56/25.80 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e21) (e22)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H1a9. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H1aa. % 25.56/25.80 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 25.56/25.80 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 25.56/25.80 congruence. % 25.56/25.80 apply (zenon_L13_); trivial. % 25.56/25.80 apply zenon_H1ab. apply refl_equal. % 25.56/25.80 apply zenon_H1ab. apply refl_equal. % 25.56/25.80 apply zenon_H2be. apply sym_equal. exact zenon_H84. % 25.56/25.80 (* end of lemma zenon_L143_ *) % 25.56/25.80 assert (zenon_L144_ : ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op1 (e13) (e11)) = (e10)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((e20) = (h4 (op1 (e13) (e11))))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H13 zenon_H154 zenon_H14 zenon_H2bf. % 25.56/25.80 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H2c0 | zenon_intro zenon_H2c1 ]. % 25.56/25.80 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((e20) = (h4 (op1 (e13) (e11))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2bf. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2c0. % 25.56/25.80 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2c1]. % 25.56/25.80 cut (((h4 (op1 (e13) (e11))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((h4 (op1 (e13) (e11))) = (e20))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2c2. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H13. % 25.56/25.80 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 25.56/25.80 cut (((h4 (e10)) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H2c0 | zenon_intro zenon_H2c1 ]. % 25.56/25.80 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((h4 (e10)) = (h4 (op1 (e13) (e11))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2c3. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2c0. % 25.56/25.80 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2c1]. % 25.56/25.80 cut (((h4 (op1 (e13) (e11))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H2c4]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2c5]. % 25.56/25.80 congruence. % 25.56/25.80 exact (zenon_H2c5 zenon_H154). % 25.56/25.80 apply zenon_H2c1. apply refl_equal. % 25.56/25.80 apply zenon_H2c1. apply refl_equal. % 25.56/25.80 apply zenon_H15. apply sym_equal. exact zenon_H14. % 25.56/25.80 apply zenon_H2c1. apply refl_equal. % 25.56/25.80 apply zenon_H2c1. apply refl_equal. % 25.56/25.80 (* end of lemma zenon_L144_ *) % 25.56/25.80 assert (zenon_L145_ : ((op2 (e23) (e21)) = (e20)) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((op1 (e13) (e11)) = (e10)) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H1a7 zenon_H208 zenon_Hac zenon_H4e zenon_H13 zenon_H14 zenon_H154 zenon_H2c6. % 25.56/25.80 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H2c7 | zenon_intro zenon_H2c8 ]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2c6. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2c7. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2c9]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((op2 (e23) (e21)) = (e20)) = ((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2c9. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H1a7. % 25.56/25.80 cut (((e20) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2bf]. % 25.56/25.80 cut (((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2ca]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H2c7 | zenon_intro zenon_H2c8 ]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2ca. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2c7. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2cb]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 25.56/25.80 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 25.56/25.80 congruence. % 25.56/25.80 exact (zenon_H214 zenon_H208). % 25.56/25.80 apply (zenon_L31_); trivial. % 25.56/25.80 apply zenon_H2c8. apply refl_equal. % 25.56/25.80 apply zenon_H2c8. apply refl_equal. % 25.56/25.80 apply (zenon_L144_); trivial. % 25.56/25.80 apply zenon_H2c8. apply refl_equal. % 25.56/25.80 apply zenon_H2c8. apply refl_equal. % 25.56/25.80 (* end of lemma zenon_L145_ *) % 25.56/25.80 assert (zenon_L146_ : (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e13)) = (op1 (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 (e11) (e12)) = (op1 (e13) (e12)))) -> ((op2 (e23) (e21)) = (e20)) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H189 zenon_H10c zenon_H1c zenon_H43 zenon_H3c zenon_H2c zenon_H49 zenon_H15d zenon_H1a7 zenon_H208 zenon_Hac zenon_H4e zenon_H13 zenon_H14 zenon_H2c6 zenon_H86 zenon_H14d zenon_H161 zenon_H1d zenon_H18 zenon_H19 zenon_H174. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H189); [ zenon_intro zenon_H10d | zenon_intro zenon_H18c ]. % 25.56/25.80 apply (zenon_L47_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H1e | zenon_intro zenon_H18d ]. % 25.56/25.80 apply (zenon_L3_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H18d); [ zenon_intro zenon_H147 | zenon_intro zenon_H173 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H14c | zenon_intro zenon_H162 ]. % 25.56/25.80 apply (zenon_L57_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H154 | zenon_intro zenon_H163 ]. % 25.56/25.80 apply (zenon_L145_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H15c | zenon_intro zenon_H33 ]. % 25.56/25.80 apply (zenon_L60_); trivial. % 25.56/25.80 apply (zenon_L12_); trivial. % 25.56/25.80 apply (zenon_L67_); trivial. % 25.56/25.80 (* end of lemma zenon_L146_ *) % 25.56/25.80 assert (zenon_L147_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op2 (e21) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/((op2 (e21) (e23)) = (e20))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op1 (e11) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/((op1 (e11) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e13) (e10)) = (e10))\/(((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e11) (e13)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e21) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H80 zenon_H43 zenon_H18 zenon_H3c zenon_H2c zenon_H19 zenon_H49 zenon_H1d zenon_H24 zenon_H1c zenon_H1da zenon_He2 zenon_H25e zenon_H189 zenon_H10c zenon_H15d zenon_H208 zenon_Hac zenon_H13 zenon_H2c6 zenon_H14d zenon_H161 zenon_H174 zenon_H2cc zenon_H2cd zenon_H9c zenon_He8 zenon_H1d8 zenon_Hec zenon_H82 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1da); [ zenon_intro zenon_He3 | zenon_intro zenon_H1db ]. % 25.56/25.80 apply (zenon_L39_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1db); [ zenon_intro zenon_H52 | zenon_intro zenon_H1dc ]. % 25.56/25.80 apply (zenon_L14_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1dc); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1d4 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1d8); [ zenon_intro zenon_He9 | zenon_intro zenon_H1dd ]. % 25.56/25.80 apply (zenon_L40_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1dd); [ zenon_intro zenon_H9d | zenon_intro zenon_H1de ]. % 25.56/25.80 apply (zenon_L27_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1de); [ zenon_intro zenon_Hed | zenon_intro zenon_H69 ]. % 25.56/25.80 apply (zenon_L41_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2cd); [ zenon_intro zenon_H2cf | zenon_intro zenon_H2ce ]. % 25.56/25.80 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H269 ]. % 25.56/25.80 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2cc. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2d0. % 25.56/25.80 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 25.56/25.80 cut (((op2 (e23) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2d1]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) = ((op2 (e23) (e20)) = (op2 (e20) (e20)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2d1. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H14. % 25.56/25.80 cut (((op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2bd]. % 25.56/25.80 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_H2d0 | zenon_intro zenon_H269 ]. % 25.56/25.80 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e20) = (op2 (e23) (e20)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2d2. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2d0. % 25.56/25.80 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 25.56/25.80 cut (((op2 (e23) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2d3]. % 25.56/25.80 congruence. % 25.56/25.80 exact (zenon_H2d3 zenon_H2cf). % 25.56/25.80 apply zenon_H269. apply refl_equal. % 25.56/25.80 apply zenon_H269. apply refl_equal. % 25.56/25.80 apply (zenon_L143_); trivial. % 25.56/25.80 apply zenon_H269. apply refl_equal. % 25.56/25.80 apply zenon_H269. apply refl_equal. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2ce); [ zenon_intro zenon_H1a7 | zenon_intro zenon_H2d4 ]. % 25.56/25.80 apply (zenon_L146_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2d4); [ zenon_intro zenon_H25d | zenon_intro zenon_H67 ]. % 25.56/25.80 apply (zenon_L121_); trivial. % 25.56/25.80 apply (zenon_L20_); trivial. % 25.56/25.80 apply (zenon_L89_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.80 apply (zenon_L3_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.80 apply (zenon_L4_); trivial. % 25.56/25.80 apply (zenon_L12_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.80 apply (zenon_L14_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.80 apply (zenon_L15_); trivial. % 25.56/25.80 apply (zenon_L23_); trivial. % 25.56/25.80 (* end of lemma zenon_L147_ *) % 25.56/25.80 assert (zenon_L148_ : (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2d5 zenon_H167 zenon_H2d6. % 25.56/25.80 cut (((op1 (e11) (e11)) = (e13)) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2d5. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H167. % 25.56/25.80 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2d7]. % 25.56/25.80 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 25.56/25.80 congruence. % 25.56/25.80 apply zenon_H21. apply refl_equal. % 25.56/25.80 apply zenon_H2d7. apply sym_equal. exact zenon_H2d6. % 25.56/25.80 (* end of lemma zenon_L148_ *) % 25.56/25.80 assert (zenon_L149_ : ((h4 (e13)) = (e23)) -> ((op1 (e13) (e12)) = (e13)) -> (~((e23) = (h4 (op1 (e13) (e12))))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H208 zenon_H247 zenon_H2d8. % 25.56/25.80 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H2da ]. % 25.56/25.80 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((e23) = (h4 (op1 (e13) (e12))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2d8. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2d9. % 25.56/25.80 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 25.56/25.80 cut (((h4 (op1 (e13) (e12))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H2db]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e13) (e12))) = (e23))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2db. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H208. % 25.56/25.80 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H5e]. % 25.56/25.80 cut (((h4 (e13)) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2dc]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H2d9 | zenon_intro zenon_H2da ]. % 25.56/25.80 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((h4 (e13)) = (h4 (op1 (e13) (e12))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2dc. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2d9. % 25.56/25.80 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 25.56/25.80 cut (((h4 (op1 (e13) (e12))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2dd]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((op1 (e13) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H2de]. % 25.56/25.80 congruence. % 25.56/25.80 exact (zenon_H2de zenon_H247). % 25.56/25.80 apply zenon_H2da. apply refl_equal. % 25.56/25.80 apply zenon_H2da. apply refl_equal. % 25.56/25.80 apply zenon_H5e. apply refl_equal. % 25.56/25.80 apply zenon_H2da. apply refl_equal. % 25.56/25.80 apply zenon_H2da. apply refl_equal. % 25.56/25.80 (* end of lemma zenon_L149_ *) % 25.56/25.80 assert (zenon_L150_ : ((op2 (e23) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e13)) = (e23)) -> ((op1 (e13) (e12)) = (e13)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H267 zenon_Hbe zenon_H4d zenon_H208 zenon_H247 zenon_H2df. % 25.56/25.80 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H2e0 | zenon_intro zenon_H2e1 ]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2df. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2e0. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2e1]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2e2]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((op2 (e23) (e22)) = (e23)) = ((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2e2. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H267. % 25.56/25.80 cut (((e23) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2d8]. % 25.56/25.80 cut (((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2e3]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H2e0 | zenon_intro zenon_H2e1 ]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2e3. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2e0. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H2e1]. % 25.56/25.80 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2e4]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 25.56/25.80 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H214]. % 25.56/25.80 congruence. % 25.56/25.80 exact (zenon_H214 zenon_H208). % 25.56/25.80 apply (zenon_L50_); trivial. % 25.56/25.80 apply zenon_H2e1. apply refl_equal. % 25.56/25.80 apply zenon_H2e1. apply refl_equal. % 25.56/25.80 apply (zenon_L149_); trivial. % 25.56/25.80 apply zenon_H2e1. apply refl_equal. % 25.56/25.80 apply zenon_H2e1. apply refl_equal. % 25.56/25.80 (* end of lemma zenon_L150_ *) % 25.56/25.80 assert (zenon_L151_ : (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (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 (e11) (e11)) = (e13)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((op2 (e23) (e22)) = (e23)) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((op1 (e11) (e13)) = (e12)) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2e5 zenon_H245 zenon_H242 zenon_Hae zenon_H137 zenon_H19 zenon_H1d zenon_H15d zenon_H249 zenon_H167 zenon_H2d5 zenon_H2df zenon_H208 zenon_H4d zenon_Hbe zenon_H267 zenon_Hb8 zenon_H18 zenon_H35. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2e5); [ zenon_intro zenon_H246 | zenon_intro zenon_H2e6 ]. % 25.56/25.80 apply (zenon_L119_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H2d6 | zenon_intro zenon_H2e7 ]. % 25.56/25.80 apply (zenon_L148_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H2e7); [ zenon_intro zenon_H247 | zenon_intro zenon_H1e5 ]. % 25.56/25.80 apply (zenon_L150_); trivial. % 25.56/25.80 apply (zenon_L93_); trivial. % 25.56/25.80 (* end of lemma zenon_L151_ *) % 25.56/25.80 assert (zenon_L152_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op2 (e23) (e22)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e13)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e10)) = (e13))\/(((op1 (e13) (e11)) = (e13))\/(((op1 (e13) (e12)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H49 zenon_H2c zenon_H267 zenon_Hbe zenon_H4d zenon_H208 zenon_H2df zenon_H2d5 zenon_H167 zenon_H249 zenon_H15d zenon_H1d zenon_H137 zenon_Hae zenon_H242 zenon_H245 zenon_H2e5 zenon_H16d zenon_H18 zenon_H19 zenon_Hb8. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H2d | zenon_intro zenon_H4a ]. % 25.56/25.80 apply (zenon_L7_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H4a); [ zenon_intro zenon_H35 | zenon_intro zenon_H4b ]. % 25.56/25.80 apply (zenon_L151_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H3b | zenon_intro zenon_H42 ]. % 25.56/25.80 apply (zenon_L65_); trivial. % 25.56/25.80 apply (zenon_L34_); trivial. % 25.56/25.80 (* end of lemma zenon_L152_ *) % 25.56/25.80 assert (zenon_L153_ : (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e12) (e12)) = (e13))\/((op1 (e13) (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) (e12)))) -> (~((op1 (e12) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (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 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((e12) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((e10) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (op1 (e13) (e13)) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (e13) (e13)) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((e20) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H80 zenon_Hba zenon_H82 zenon_Hb8 zenon_H1e8 zenon_Hde zenon_H2e5 zenon_H245 zenon_H242 zenon_H137 zenon_H15d zenon_H249 zenon_H2d5 zenon_H2df zenon_H208 zenon_Hbe zenon_H262 zenon_H19c zenon_H25e zenon_H26a zenon_H1e2 zenon_H16d zenon_Ha7 zenon_Ha2 zenon_Hc0 zenon_H1c zenon_H24 zenon_H1d zenon_H49 zenon_H19 zenon_H2c zenon_H3c zenon_H18 zenon_H43 zenon_H9c zenon_H97 zenon_Hc1 zenon_H51 zenon_H58 zenon_H14 zenon_H7d zenon_H4e zenon_H60 zenon_H70 zenon_H4d zenon_H77. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.80 apply (zenon_L26_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.80 apply (zenon_L27_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H82); [ zenon_intro zenon_H86 | zenon_intro zenon_H85 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc0); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Hc4 ]. % 25.56/25.80 apply (zenon_L29_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Hc5 ]. % 25.56/25.80 apply (zenon_L30_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc5); [ zenon_intro zenon_Hae | zenon_intro zenon_H42 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1e8); [ zenon_intro zenon_Hdd | zenon_intro zenon_H1e9 ]. % 25.56/25.80 apply (zenon_L38_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H167 | zenon_intro zenon_H1ea ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H26a); [ zenon_intro zenon_H25d | zenon_intro zenon_H26b ]. % 25.56/25.80 apply (zenon_L121_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H26b); [ zenon_intro zenon_H19d | zenon_intro zenon_H26c ]. % 25.56/25.80 apply (zenon_L76_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H26c); [ zenon_intro zenon_H263 | zenon_intro zenon_H267 ]. % 25.56/25.80 apply (zenon_L122_); trivial. % 25.56/25.80 apply (zenon_L152_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1ea); [ zenon_intro zenon_H1e1 | zenon_intro zenon_H1e5 ]. % 25.56/25.80 apply (zenon_L92_); trivial. % 25.56/25.80 apply (zenon_L94_); trivial. % 25.56/25.80 apply (zenon_L34_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H85); [ zenon_intro zenon_H1e | zenon_intro zenon_H93 ]. % 25.56/25.80 apply (zenon_L3_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H93); [ zenon_intro zenon_H23 | zenon_intro zenon_H33 ]. % 25.56/25.80 apply (zenon_L4_); trivial. % 25.56/25.80 apply (zenon_L12_); trivial. % 25.56/25.80 apply (zenon_L35_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.80 apply (zenon_L14_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.80 apply (zenon_L15_); trivial. % 25.56/25.80 apply (zenon_L23_); trivial. % 25.56/25.80 (* end of lemma zenon_L153_ *) % 25.56/25.80 assert (zenon_L154_ : (~((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e11) = (op1 (e13) (e13))) -> ((h4 (e13)) = (e23)) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2e8 zenon_Hac zenon_H19 zenon_H208. % 25.56/25.80 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2e8. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_Hac. % 25.56/25.80 cut (((op2 (e23) (e23)) = (op2 (h4 (e13)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2e9]. % 25.56/25.80 cut (((h4 (e11)) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2ea]. % 25.56/25.80 congruence. % 25.56/25.80 elim (classic ((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [ zenon_intro zenon_H2eb | zenon_intro zenon_H2ec ]. % 25.56/25.80 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13)))) = ((h4 (e11)) = (h4 (op1 (e13) (e13))))). % 25.56/25.80 intro zenon_D_pnotp. % 25.56/25.80 apply zenon_H2ea. % 25.56/25.80 rewrite <- zenon_D_pnotp. % 25.56/25.80 exact zenon_H2eb. % 25.56/25.80 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 25.56/25.80 cut (((h4 (op1 (e13) (e13))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 25.56/25.80 congruence. % 25.56/25.80 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 25.56/25.80 congruence. % 25.56/25.80 apply zenon_H1b. apply sym_equal. exact zenon_H19. % 25.56/25.80 apply zenon_H2ec. apply refl_equal. % 25.56/25.80 apply zenon_H2ec. apply refl_equal. % 25.56/25.80 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 25.56/25.80 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 25.56/25.80 congruence. % 25.56/25.80 apply zenon_H241. apply sym_equal. exact zenon_H208. % 25.56/25.80 apply zenon_H241. apply sym_equal. exact zenon_H208. % 25.56/25.80 (* end of lemma zenon_L154_ *) % 25.56/25.80 assert (zenon_L155_ : (~(((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (op2 (e23) (e23)) (e23)))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2ee zenon_H13 zenon_H14. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2ee). zenon_intro zenon_H12. zenon_intro zenon_H2ef. % 25.56/25.80 apply (zenon_L1_); trivial. % 25.56/25.80 (* end of lemma zenon_L155_ *) % 25.56/25.80 assert (zenon_L156_ : (~(((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2f0 zenon_Hac zenon_H4e. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2f0). zenon_intro zenon_H2f2. zenon_intro zenon_H2f1. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2f1). zenon_intro zenon_Hab. zenon_intro zenon_H2f3. % 25.56/25.80 apply (zenon_L31_); trivial. % 25.56/25.80 (* end of lemma zenon_L156_ *) % 25.56/25.80 assert (zenon_L157_ : (~(((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))) -> ((h4 (e12)) = (op2 (op2 (e23) (e23)) (e23))) -> ((e22) = (op2 (op2 (e23) (e23)) (e23))) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2f4 zenon_Hbe zenon_H4d. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2f4). zenon_intro zenon_H2f6. zenon_intro zenon_H2f5. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2f5). zenon_intro zenon_H2f8. zenon_intro zenon_H2f7. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2f7). zenon_intro zenon_H11e. zenon_intro zenon_H2f9. % 25.56/25.80 apply (zenon_L50_); trivial. % 25.56/25.80 (* end of lemma zenon_L157_ *) % 25.56/25.80 assert (zenon_L158_ : (~(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23)))))) -> ((h4 (e13)) = (e23)) -> False). % 25.56/25.80 do 0 intro. intros zenon_H2fa zenon_H208. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2fa). zenon_intro zenon_H2fc. zenon_intro zenon_H2fb. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2fb). zenon_intro zenon_H2fe. zenon_intro zenon_H2fd. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H2fd). zenon_intro zenon_H2ff. zenon_intro zenon_H214. % 25.56/25.80 exact (zenon_H214 zenon_H208). % 25.56/25.80 (* end of lemma zenon_L158_ *) % 25.56/25.80 apply NNPP. intro zenon_G. % 25.56/25.80 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H301. zenon_intro zenon_H300. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H300). zenon_intro zenon_H303. zenon_intro zenon_H302. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H302). zenon_intro zenon_H305. zenon_intro zenon_H304. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H304). zenon_intro zenon_H215. zenon_intro zenon_H306. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H306). zenon_intro zenon_H180. zenon_intro zenon_H307. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H309. zenon_intro zenon_H308. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H308). zenon_intro zenon_H30b. zenon_intro zenon_H30a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H30a). zenon_intro zenon_H30d. zenon_intro zenon_H30c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H30c). zenon_intro zenon_H30f. zenon_intro zenon_H30e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H30e). zenon_intro zenon_H16a. zenon_intro zenon_H310. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_H312. zenon_intro zenon_H311. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H311). zenon_intro zenon_H314. zenon_intro zenon_H313. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H313). zenon_intro zenon_H316. zenon_intro zenon_H315. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H315). zenon_intro zenon_H318. zenon_intro zenon_H317. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H317). zenon_intro zenon_H249. zenon_intro zenon_H319. % 25.56/25.80 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H31b. zenon_intro zenon_H31a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H31a). zenon_intro zenon_H31d. zenon_intro zenon_H31c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H31c). zenon_intro zenon_H31f. zenon_intro zenon_H31e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H31e). zenon_intro zenon_H187. zenon_intro zenon_H320. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H320). zenon_intro zenon_Hbf. zenon_intro zenon_H321. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H323. zenon_intro zenon_H322. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H322). zenon_intro zenon_H325. zenon_intro zenon_H324. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H324). zenon_intro zenon_H24c. zenon_intro zenon_H326. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H326). zenon_intro zenon_H189. zenon_intro zenon_H327. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_H329. zenon_intro zenon_H328. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H32b. zenon_intro zenon_H32a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H32a). zenon_intro zenon_H32d. zenon_intro zenon_H32c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H32f. zenon_intro zenon_H32e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H32e). zenon_intro zenon_H331. zenon_intro zenon_H330. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H333. zenon_intro zenon_H332. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H332). zenon_intro zenon_H335. zenon_intro zenon_H334. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H337. zenon_intro zenon_H336. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H336). zenon_intro zenon_H339. zenon_intro zenon_H338. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H188. zenon_intro zenon_H33a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H13d. zenon_intro zenon_H33b. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_H33d. zenon_intro zenon_H33c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H33c). zenon_intro zenon_H33f. zenon_intro zenon_H33e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H33e). zenon_intro zenon_H341. zenon_intro zenon_H340. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H340). zenon_intro zenon_H343. zenon_intro zenon_H342. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H342). zenon_intro zenon_H161. zenon_intro zenon_H344. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H344). zenon_intro zenon_H296. zenon_intro zenon_H345. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H345). zenon_intro zenon_H347. zenon_intro zenon_H346. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H346). zenon_intro zenon_H349. zenon_intro zenon_H348. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H2b7. zenon_intro zenon_H34a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H49. zenon_intro zenon_H34b. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H34b). zenon_intro zenon_H2e5. zenon_intro zenon_H34c. % 25.56/25.80 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H34e. zenon_intro zenon_H34d. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H34d). zenon_intro zenon_H350. zenon_intro zenon_H34f. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H34f). zenon_intro zenon_H352. zenon_intro zenon_H351. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H351). zenon_intro zenon_H218. zenon_intro zenon_H353. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H353). zenon_intro zenon_H103. zenon_intro zenon_H354. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H356. zenon_intro zenon_H355. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H355). zenon_intro zenon_H358. zenon_intro zenon_H357. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H357). zenon_intro zenon_H35a. zenon_intro zenon_H359. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_H35c. zenon_intro zenon_H35b. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_H1cd. zenon_intro zenon_H35d. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H35f. zenon_intro zenon_H35e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H35e). zenon_intro zenon_H361. zenon_intro zenon_H360. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H360). zenon_intro zenon_H363. zenon_intro zenon_H362. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H362). zenon_intro zenon_H1c5. zenon_intro zenon_H364. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H364). zenon_intro zenon_H26a. zenon_intro zenon_H365. % 25.56/25.80 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H367. zenon_intro zenon_H366. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H366). zenon_intro zenon_H369. zenon_intro zenon_H368. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H368). zenon_intro zenon_H36b. zenon_intro zenon_H36a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H36a). zenon_intro zenon_H36d. zenon_intro zenon_H36c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H36c). zenon_intro zenon_Hbc. zenon_intro zenon_H36e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H36e). zenon_intro zenon_H370. zenon_intro zenon_H36f. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H36f). zenon_intro zenon_H372. zenon_intro zenon_H371. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H371). zenon_intro zenon_H26d. zenon_intro zenon_H373. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H373). zenon_intro zenon_H1da. zenon_intro zenon_H374. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_H376. zenon_intro zenon_H375. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H375). zenon_intro zenon_H378. zenon_intro zenon_H377. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H377). zenon_intro zenon_H37a. zenon_intro zenon_H379. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H379). zenon_intro zenon_H1d8. zenon_intro zenon_H37b. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H37b). zenon_intro zenon_H37d. zenon_intro zenon_H37c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_H37f. zenon_intro zenon_H37e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_H381. zenon_intro zenon_H380. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_H383. zenon_intro zenon_H382. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H382). zenon_intro zenon_H385. zenon_intro zenon_H384. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H384). zenon_intro zenon_H1d9. zenon_intro zenon_H386. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H386). zenon_intro zenon_H1a2. zenon_intro zenon_H387. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H387). zenon_intro zenon_H389. zenon_intro zenon_H388. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H388). zenon_intro zenon_H38b. zenon_intro zenon_H38a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_H38d. zenon_intro zenon_H38c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H38c). zenon_intro zenon_H38f. zenon_intro zenon_H38e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H2cd. zenon_intro zenon_H390. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H299. zenon_intro zenon_H391. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H391). zenon_intro zenon_H393. zenon_intro zenon_H392. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_H395. zenon_intro zenon_H394. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H2ba. zenon_intro zenon_H396. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H396). zenon_intro zenon_H7d. zenon_intro zenon_H397. % 25.56/25.80 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H399. zenon_intro zenon_H398. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H398). zenon_intro zenon_H39b. zenon_intro zenon_H39a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H39a). zenon_intro zenon_H14d. zenon_intro zenon_H39c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H118. zenon_intro zenon_H39d. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H39d). zenon_intro zenon_H39f. zenon_intro zenon_H39e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H39e). zenon_intro zenon_H3a1. zenon_intro zenon_H3a0. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H3a3. zenon_intro zenon_H3a2. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3a2). zenon_intro zenon_H3a5. zenon_intro zenon_H3a4. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3a4). zenon_intro zenon_H2b1. zenon_intro zenon_H3a6. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3a6). zenon_intro zenon_H166. zenon_intro zenon_H3a7. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3a7). zenon_intro zenon_H2d5. zenon_intro zenon_H3a8. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3a8). zenon_intro zenon_H156. zenon_intro zenon_H3a9. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3a9). zenon_intro zenon_H3ab. zenon_intro zenon_H3aa. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3aa). zenon_intro zenon_Hb0. zenon_intro zenon_H3ac. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ac). zenon_intro zenon_H3ae. zenon_intro zenon_H3ad. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ad). zenon_intro zenon_H24. zenon_intro zenon_H3af. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3af). zenon_intro zenon_H15d. zenon_intro zenon_H3b0. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b0). zenon_intro zenon_H242. zenon_intro zenon_H3b1. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b1). zenon_intro zenon_H2c. zenon_intro zenon_H3b2. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b2). zenon_intro zenon_H3c. zenon_intro zenon_H3b3. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b3). zenon_intro zenon_H43. zenon_intro zenon_H3b4. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b4). zenon_intro zenon_H16d. zenon_intro zenon_H3b5. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b5). zenon_intro zenon_Hb8. zenon_intro zenon_H3b6. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b6). zenon_intro zenon_H16f. zenon_intro zenon_H3b7. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b7). zenon_intro zenon_H3b9. zenon_intro zenon_H3b8. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3b8). zenon_intro zenon_H3bb. zenon_intro zenon_H3ba. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ba). zenon_intro zenon_H1fe. zenon_intro zenon_H3bc. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_H3be. zenon_intro zenon_H3bd. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3bd). zenon_intro zenon_H3c0. zenon_intro zenon_H3bf. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3bf). zenon_intro zenon_H3c2. zenon_intro zenon_H3c1. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c1). zenon_intro zenon_H17d. zenon_intro zenon_H3c3. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c3). zenon_intro zenon_H10c. zenon_intro zenon_H3c4. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c4). zenon_intro zenon_H178. zenon_intro zenon_H3c5. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c5). zenon_intro zenon_H1c. zenon_intro zenon_H3c6. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c6). zenon_intro zenon_Ha7. zenon_intro zenon_H3c7. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H174. zenon_intro zenon_H3c8. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H3ca. zenon_intro zenon_H3c9. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3c9). zenon_intro zenon_H3cc. zenon_intro zenon_H3cb. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3cb). zenon_intro zenon_H3ce. zenon_intro zenon_H3cd. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3cd). zenon_intro zenon_H133. zenon_intro zenon_H3cf. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3cf). zenon_intro zenon_H3d1. zenon_intro zenon_H3d0. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3d0). zenon_intro zenon_H3d3. zenon_intro zenon_H3d2. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3d2). zenon_intro zenon_H3d5. zenon_intro zenon_H3d4. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3d4). zenon_intro zenon_H245. zenon_intro zenon_H3d6. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3d6). zenon_intro zenon_H183. zenon_intro zenon_H3d7. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_H3d9. zenon_intro zenon_H3d8. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3d8). zenon_intro zenon_H3da. zenon_intro zenon_H137. % 25.56/25.80 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H3dc. zenon_intro zenon_H3db. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3db). zenon_intro zenon_H3de. zenon_intro zenon_H3dd. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3dd). zenon_intro zenon_H2cc. zenon_intro zenon_H3df. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_Hf8. zenon_intro zenon_H3e0. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_H3e2. zenon_intro zenon_H3e1. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3e1). zenon_intro zenon_H3e4. zenon_intro zenon_H3e3. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3e3). zenon_intro zenon_H3e6. zenon_intro zenon_H3e5. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3e5). zenon_intro zenon_H3e8. zenon_intro zenon_H3e7. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H1be. zenon_intro zenon_H3e9. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3e9). zenon_intro zenon_H1ca. zenon_intro zenon_H3ea. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ea). zenon_intro zenon_H1c2. zenon_intro zenon_H3eb. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3eb). zenon_intro zenon_H1ac. zenon_intro zenon_H3ec. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ec). zenon_intro zenon_H3ee. zenon_intro zenon_H3ed. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ed). zenon_intro zenon_Hb5. zenon_intro zenon_H3ef. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ef). zenon_intro zenon_H3f1. zenon_intro zenon_H3f0. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f0). zenon_intro zenon_H58. zenon_intro zenon_H3f2. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f2). zenon_intro zenon_H25e. zenon_intro zenon_H3f3. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f3). zenon_intro zenon_H262. zenon_intro zenon_H3f4. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f4). zenon_intro zenon_H60. zenon_intro zenon_H3f5. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f5). zenon_intro zenon_H70. zenon_intro zenon_H3f6. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f6). zenon_intro zenon_H77. zenon_intro zenon_H3f7. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f7). zenon_intro zenon_H1f2. zenon_intro zenon_H3f8. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f8). zenon_intro zenon_Hba. zenon_intro zenon_H3f9. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3f9). zenon_intro zenon_H1d0. zenon_intro zenon_H3fa. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3fa). zenon_intro zenon_H3fc. zenon_intro zenon_H3fb. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3fb). zenon_intro zenon_H3fe. zenon_intro zenon_H3fd. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3fd). zenon_intro zenon_H1f7. zenon_intro zenon_H3ff. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H3ff). zenon_intro zenon_H401. zenon_intro zenon_H400. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H400). zenon_intro zenon_H403. zenon_intro zenon_H402. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H402). zenon_intro zenon_H405. zenon_intro zenon_H404. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H404). zenon_intro zenon_H100. zenon_intro zenon_H406. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H406). zenon_intro zenon_He2. zenon_intro zenon_H407. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H407). zenon_intro zenon_He8. zenon_intro zenon_H408. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H408). zenon_intro zenon_H51. zenon_intro zenon_H409. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H409). zenon_intro zenon_H9c. zenon_intro zenon_H40a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H40a). zenon_intro zenon_Hec. zenon_intro zenon_H40b. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H40b). zenon_intro zenon_H40d. zenon_intro zenon_H40c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H40c). zenon_intro zenon_H40f. zenon_intro zenon_H40e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H40e). zenon_intro zenon_H411. zenon_intro zenon_H410. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H410). zenon_intro zenon_H198. zenon_intro zenon_H412. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H412). zenon_intro zenon_H414. zenon_intro zenon_H413. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H413). zenon_intro zenon_H416. zenon_intro zenon_H415. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H415). zenon_intro zenon_H418. zenon_intro zenon_H417. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H417). zenon_intro zenon_H265. zenon_intro zenon_H419. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H419). zenon_intro zenon_H41b. zenon_intro zenon_H41a. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H41a). zenon_intro zenon_H41d. zenon_intro zenon_H41c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H41c). zenon_intro zenon_H1b2. zenon_intro zenon_H19c. % 25.56/25.80 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H107. zenon_intro zenon_H41e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H41e). zenon_intro zenon_Ha2. zenon_intro zenon_H41f. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H41f). zenon_intro zenon_Hde. zenon_intro zenon_H420. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H420). zenon_intro zenon_H422. zenon_intro zenon_H421. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H421). zenon_intro zenon_H423. zenon_intro zenon_H1e2. % 25.56/25.80 apply (zenon_and_s _ _ ax8). zenon_intro zenon_H425. zenon_intro zenon_H424. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H424). zenon_intro zenon_H97. zenon_intro zenon_H426. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H426). zenon_intro zenon_Hd9. zenon_intro zenon_H427. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H427). zenon_intro zenon_H429. zenon_intro zenon_H428. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H428). zenon_intro zenon_H42a. zenon_intro zenon_H1ec. % 25.56/25.80 apply (zenon_and_s _ _ ax10). zenon_intro zenon_H82. zenon_intro zenon_H42b. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H42b). zenon_intro zenon_H42d. zenon_intro zenon_H42c. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H42c). zenon_intro zenon_Hc0. zenon_intro zenon_H42e. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H42e). zenon_intro zenon_H1e8. zenon_intro zenon_H42f. % 25.56/25.80 apply (zenon_and_s _ _ ax11). zenon_intro zenon_H80. zenon_intro zenon_H430. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H430). zenon_intro zenon_H432. zenon_intro zenon_H431. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H431). zenon_intro zenon_Hc1. zenon_intro zenon_H433. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H433). zenon_intro zenon_H1f4. zenon_intro zenon_H434. % 25.56/25.80 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H1d. zenon_intro zenon_H435. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H435). zenon_intro zenon_H19. zenon_intro zenon_H18. % 25.56/25.80 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H14. zenon_intro zenon_H436. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H436). zenon_intro zenon_H4e. zenon_intro zenon_H4d. % 25.56/25.80 apply (zenon_and_s _ _ ax17). zenon_intro zenon_H208. zenon_intro zenon_H437. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H437). zenon_intro zenon_H13. zenon_intro zenon_H438. % 25.56/25.80 apply (zenon_and_s _ _ zenon_H438). zenon_intro zenon_Hac. zenon_intro zenon_Hbe. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H43a. zenon_intro zenon_H439. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H439). zenon_intro zenon_H43c. zenon_intro zenon_H43b. % 25.56/25.80 apply (zenon_notor_s _ _ zenon_H43b). zenon_intro zenon_H43e. zenon_intro zenon_H43d. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H43d); [ zenon_intro zenon_H81 | zenon_intro zenon_H43f ]. % 25.56/25.80 apply (zenon_L24_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H43f); [ zenon_intro zenon_Hbd | zenon_intro zenon_H440 ]. % 25.56/25.80 apply (zenon_L36_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H440); [ zenon_intro zenon_H120 | zenon_intro zenon_H441 ]. % 25.56/25.80 apply (zenon_L101_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H441); [ zenon_intro zenon_H205 | zenon_intro zenon_H442 ]. % 25.56/25.80 apply (zenon_L108_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H442); [ zenon_intro zenon_H21b | zenon_intro zenon_H443 ]. % 25.56/25.80 apply (zenon_L112_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H443); [ zenon_intro zenon_H226 | zenon_intro zenon_H444 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H80); [ zenon_intro zenon_H84 | zenon_intro zenon_H83 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc1); [ zenon_intro zenon_H96 | zenon_intro zenon_Hc2 ]. % 25.56/25.80 apply (zenon_L26_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc2); [ zenon_intro zenon_H9d | zenon_intro zenon_Hc3 ]. % 25.56/25.80 apply (zenon_L27_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_Hc3); [ zenon_intro zenon_Hb3 | zenon_intro zenon_H76 ]. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1f4); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1f5 ]. % 25.56/25.80 apply (zenon_L37_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1f5); [ zenon_intro zenon_Hfe | zenon_intro zenon_H1f6 ]. % 25.56/25.80 apply (zenon_L113_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H1f6); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1ef ]. % 25.56/25.80 apply (zenon_L97_); trivial. % 25.56/25.80 apply (zenon_L100_); trivial. % 25.56/25.80 apply (zenon_L35_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H83); [ zenon_intro zenon_H52 | zenon_intro zenon_H94 ]. % 25.56/25.80 apply (zenon_L14_); trivial. % 25.56/25.80 apply (zenon_or_s _ _ zenon_H94); [ zenon_intro zenon_H57 | zenon_intro zenon_H67 ]. % 25.56/25.80 apply (zenon_L15_); trivial. % 25.56/25.80 apply (zenon_L23_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H444); [ zenon_intro zenon_H232 | zenon_intro zenon_H445 ]. % 25.56/25.80 apply (zenon_L114_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H445); [ zenon_intro zenon_H23b | zenon_intro zenon_H446 ]. % 25.56/25.80 apply (zenon_L116_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H446); [ zenon_intro zenon_H24e | zenon_intro zenon_H447 ]. % 25.56/25.80 apply (zenon_L125_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H447); [ zenon_intro zenon_H276 | zenon_intro zenon_H448 ]. % 25.56/25.80 apply (zenon_L132_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H448); [ zenon_intro zenon_H27c | zenon_intro zenon_H449 ]. % 25.56/25.80 apply (zenon_L133_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H449); [ zenon_intro zenon_H288 | zenon_intro zenon_H44a ]. % 25.56/25.80 apply (zenon_L136_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H44a); [ zenon_intro zenon_H2a5 | zenon_intro zenon_H44b ]. % 25.56/25.80 apply (zenon_L142_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H44b); [ zenon_intro zenon_H2c6 | zenon_intro zenon_H44c ]. % 25.56/25.80 apply (zenon_L147_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H2df | zenon_intro zenon_H44d ]. % 25.56/25.80 apply (zenon_L153_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H44d); [ zenon_intro zenon_H2e8 | zenon_intro zenon_H44e ]. % 25.56/25.80 apply (zenon_L154_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H44e); [ zenon_intro zenon_H2ee | zenon_intro zenon_H44f ]. % 25.56/25.80 apply (zenon_L155_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H44f); [ zenon_intro zenon_H2f0 | zenon_intro zenon_H450 ]. % 25.56/25.80 apply (zenon_L156_); trivial. % 25.56/25.80 apply (zenon_notand_s _ _ zenon_H450); [ zenon_intro zenon_H2f4 | zenon_intro zenon_H2fa ]. % 25.56/25.80 apply (zenon_L157_); trivial. % 25.56/25.80 apply (zenon_L158_); trivial. % 25.56/25.80 Qed. % 25.56/25.80 % SZS output end Proof % 25.56/25.80 (* END-PROOF *) % 25.56/25.80 nodes searched: 1379246 % 25.56/25.80 max branch formulas: 1977 % 25.56/25.80 proof nodes created: 12437 % 25.56/25.80 formulas created: 647938 % 25.56/25.80 %------------------------------------------------------------------------------