%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG121+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n032.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 18:29:33 EDT 2022 % Result : Theorem 19.63s 19.88s % Output : Proof 19.71s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.10 % Problem : ALG121+1 : TPTP v8.1.0. Released v2.7.0. % 0.00/0.10 % Command : run_zenon %s %d % 0.10/0.30 % Computer : n032.cluster.edu % 0.10/0.30 % Model : x86_64 x86_64 % 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.10/0.30 % Memory : 8042.1875MB % 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64 % 0.10/0.30 % CPULimit : 300 % 0.10/0.30 % WCLimit : 600 % 0.10/0.30 % DateTime : Wed Jun 8 00:45:51 EDT 2022 % 0.10/0.30 % CPUTime : % 19.63/19.88 (* PROOF-FOUND *) % 19.63/19.88 % SZS status Theorem % 19.63/19.88 (* BEGIN-PROOF *) % 19.63/19.88 % SZS output start Proof % 19.63/19.88 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))))))))))))))))))))))))))). % 19.63/19.88 Proof. % 19.63/19.88 assert (zenon_L1_ : (~((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H12 zenon_H13. % 19.63/19.88 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 19.63/19.88 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.63/19.88 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.63/19.88 (* end of lemma zenon_L1_ *) % 19.63/19.88 assert (zenon_L2_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e10) (e11)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H15 zenon_H16 zenon_H13 zenon_H17. % 19.63/19.88 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ]. % 19.63/19.88 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((op1 (e10) (e10)) = (op1 (e10) (e11)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H17. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H18. % 19.63/19.88 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 19.63/19.88 cut (((op1 (e10) (e11)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1a]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e10) (e11)) = (op1 (e10) (e10)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H1a. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H15. % 19.63/19.88 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 19.63/19.88 cut (((e11) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1b]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H18 | zenon_intro zenon_H19 ]. % 19.63/19.88 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e11) = (op1 (e10) (e11)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H1b. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H18. % 19.63/19.88 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 19.63/19.88 cut (((op1 (e10) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H1c zenon_H16). % 19.63/19.88 apply zenon_H19. apply refl_equal. % 19.63/19.88 apply zenon_H19. apply refl_equal. % 19.63/19.88 apply (zenon_L1_); trivial. % 19.63/19.88 apply zenon_H19. apply refl_equal. % 19.63/19.88 apply zenon_H19. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L2_ *) % 19.63/19.88 assert (zenon_L3_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H15 zenon_H1d zenon_H13 zenon_H1e. % 19.63/19.88 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 19.63/19.88 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((op1 (e10) (e10)) = (op1 (e10) (e12)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H1e. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H1f. % 19.63/19.88 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 19.63/19.88 cut (((op1 (e10) (e12)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H21]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e10) (e12)) = (op1 (e10) (e10)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H21. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H15. % 19.63/19.88 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 19.63/19.88 cut (((e11) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H22]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H1f | zenon_intro zenon_H20 ]. % 19.63/19.88 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e11) = (op1 (e10) (e12)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H22. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H1f. % 19.63/19.88 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H20]. % 19.63/19.88 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H23 zenon_H1d). % 19.63/19.88 apply zenon_H20. apply refl_equal. % 19.63/19.88 apply zenon_H20. apply refl_equal. % 19.63/19.88 apply (zenon_L1_); trivial. % 19.63/19.88 apply zenon_H20. apply refl_equal. % 19.63/19.88 apply zenon_H20. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L3_ *) % 19.63/19.88 assert (zenon_L4_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H15 zenon_H24 zenon_H13 zenon_H25. % 19.63/19.88 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((op1 (e10) (e10)) = (op1 (e10) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H25. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H26. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H28]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e10) (e13)) = (op1 (e10) (e10)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H28. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H15. % 19.63/19.88 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 19.63/19.88 cut (((e11) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H29]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e11) = (op1 (e10) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H29. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H26. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H2a zenon_H24). % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 apply (zenon_L1_); trivial. % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L4_ *) % 19.63/19.88 assert (zenon_L5_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))) -> ((e20) = (op2 (e23) (e23))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H2b zenon_H2c. % 19.63/19.88 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 19.63/19.88 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.63/19.88 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.63/19.88 (* end of lemma zenon_L5_ *) % 19.63/19.88 assert (zenon_L6_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H2e zenon_H2f zenon_H2c zenon_H30. % 19.63/19.88 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H31 | zenon_intro zenon_H32 ]. % 19.63/19.88 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((op2 (e20) (e20)) = (op2 (e20) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H30. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H31. % 19.63/19.88 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 19.63/19.88 cut (((op2 (e20) (e21)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H33]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e20) (e21)) = (op2 (e20) (e20)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H33. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2e. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.63/19.88 cut (((e21) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H34]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H31 | zenon_intro zenon_H32 ]. % 19.63/19.88 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e21) = (op2 (e20) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H34. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H31. % 19.63/19.88 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 19.63/19.88 cut (((op2 (e20) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H35]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H35 zenon_H2f). % 19.63/19.88 apply zenon_H32. apply refl_equal. % 19.63/19.88 apply zenon_H32. apply refl_equal. % 19.63/19.88 apply (zenon_L5_); trivial. % 19.63/19.88 apply zenon_H32. apply refl_equal. % 19.63/19.88 apply zenon_H32. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L6_ *) % 19.63/19.88 assert (zenon_L7_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H2e zenon_H36 zenon_H2c zenon_H37. % 19.63/19.88 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ]. % 19.63/19.88 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((op2 (e20) (e20)) = (op2 (e20) (e22)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H37. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H38. % 19.63/19.88 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 19.63/19.88 cut (((op2 (e20) (e22)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H3a]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e20) (e22)) = (op2 (e20) (e20)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H3a. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2e. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.63/19.88 cut (((e21) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e20) (e22)) = (op2 (e20) (e22)))); [ zenon_intro zenon_H38 | zenon_intro zenon_H39 ]. % 19.63/19.88 cut (((op2 (e20) (e22)) = (op2 (e20) (e22))) = ((e21) = (op2 (e20) (e22)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H3b. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H38. % 19.63/19.88 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 19.63/19.88 cut (((op2 (e20) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H3c zenon_H36). % 19.63/19.88 apply zenon_H39. apply refl_equal. % 19.63/19.88 apply zenon_H39. apply refl_equal. % 19.63/19.88 apply (zenon_L5_); trivial. % 19.63/19.88 apply zenon_H39. apply refl_equal. % 19.63/19.88 apply zenon_H39. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L7_ *) % 19.63/19.88 assert (zenon_L8_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H2e zenon_H3d zenon_H2c zenon_H3e. % 19.63/19.88 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((op2 (e20) (e20)) = (op2 (e20) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H3e. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H3f. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H41]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e20) (e23)) = (op2 (e20) (e20)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H41. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2e. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.63/19.88 cut (((e21) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e21) = (op2 (e20) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H42. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H3f. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H43 zenon_H3d). % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 apply (zenon_L5_); trivial. % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L8_ *) % 19.63/19.88 assert (zenon_L9_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H44 zenon_H45 zenon_H30 zenon_H37 zenon_H2e zenon_H2c zenon_H3e. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 19.63/19.88 exact (zenon_H45 zenon_H47). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H2f | zenon_intro zenon_H48 ]. % 19.63/19.88 apply (zenon_L6_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H36 | zenon_intro zenon_H3d ]. % 19.63/19.88 apply (zenon_L7_); trivial. % 19.63/19.88 apply (zenon_L8_); trivial. % 19.63/19.88 (* end of lemma zenon_L9_ *) % 19.63/19.88 assert (zenon_L10_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e10)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H49 zenon_H4a zenon_H17 zenon_H1e zenon_H15 zenon_H13 zenon_H25. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 19.63/19.88 exact (zenon_H4a zenon_H4c). % 19.63/19.88 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H16 | zenon_intro zenon_H4d ]. % 19.63/19.88 apply (zenon_L2_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H1d | zenon_intro zenon_H24 ]. % 19.63/19.88 apply (zenon_L3_); trivial. % 19.63/19.88 apply (zenon_L4_); trivial. % 19.63/19.88 (* end of lemma zenon_L10_ *) % 19.63/19.88 assert (zenon_L11_ : (~((h4 (e10)) = (e20))) -> ((h4 (e10)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (e23))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H4e zenon_H4f zenon_H2c. % 19.63/19.88 cut (((h4 (e10)) = (op2 (e23) (e23))) = ((h4 (e10)) = (e20))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H4e. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H4f. % 19.63/19.88 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 19.63/19.88 cut (((h4 (e10)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H50. apply refl_equal. % 19.63/19.88 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.63/19.88 (* end of lemma zenon_L11_ *) % 19.63/19.88 assert (zenon_L12_ : (~((h4 (e11)) = (e21))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H51 zenon_H52 zenon_H2e. % 19.63/19.88 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (e11)) = (e21))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H51. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H52. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 19.63/19.88 cut (((h4 (e11)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H54]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H54. apply refl_equal. % 19.63/19.88 apply zenon_H53. apply sym_equal. exact zenon_H2e. % 19.63/19.88 (* end of lemma zenon_L12_ *) % 19.63/19.88 assert (zenon_L13_ : (~((e20) = (e20))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H55. % 19.63/19.88 apply zenon_H55. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L13_ *) % 19.63/19.88 assert (zenon_L14_ : ((op2 (e20) (e21)) = (e20)) -> ((op2 (e20) (e21)) = (e22)) -> (~((e20) = (e22))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H56 zenon_H57 zenon_H58. % 19.63/19.88 elim (classic ((e22) = (e22))); [ zenon_intro zenon_H59 | zenon_intro zenon_H5a ]. % 19.63/19.88 cut (((e22) = (e22)) = ((e20) = (e22))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H58. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H59. % 19.63/19.88 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 19.63/19.88 cut (((e22) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((op2 (e20) (e21)) = (e20)) = ((e22) = (e20))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H5b. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H56. % 19.63/19.88 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 19.63/19.88 cut (((op2 (e20) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H5c zenon_H57). % 19.63/19.88 apply zenon_H55. apply refl_equal. % 19.63/19.88 apply zenon_H5a. apply refl_equal. % 19.63/19.88 apply zenon_H5a. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L14_ *) % 19.63/19.88 assert (zenon_L15_ : (~((e10) = (e10))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H5d. % 19.63/19.88 apply zenon_H5d. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L15_ *) % 19.63/19.88 assert (zenon_L16_ : ((op1 (e10) (e11)) = (e10)) -> ((op1 (e10) (e11)) = (e12)) -> (~((e10) = (e12))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H5e zenon_H5f zenon_H60. % 19.63/19.88 elim (classic ((e12) = (e12))); [ zenon_intro zenon_H61 | zenon_intro zenon_H62 ]. % 19.63/19.88 cut (((e12) = (e12)) = ((e10) = (e12))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H60. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H61. % 19.63/19.88 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 19.63/19.88 cut (((e12) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H63]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((op1 (e10) (e11)) = (e10)) = ((e12) = (e10))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H63. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H5e. % 19.63/19.88 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 19.63/19.88 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H64 zenon_H5f). % 19.63/19.88 apply zenon_H5d. apply refl_equal. % 19.63/19.88 apply zenon_H62. apply refl_equal. % 19.63/19.88 apply zenon_H62. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L16_ *) % 19.63/19.88 assert (zenon_L17_ : (~((h4 (e12)) = (e22))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H65 zenon_H66 zenon_H67. % 19.63/19.88 cut (((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((h4 (e12)) = (e22))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H65. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H66. % 19.63/19.88 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 19.63/19.88 cut (((h4 (e12)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H69]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H69. apply refl_equal. % 19.63/19.88 apply zenon_H68. apply sym_equal. exact zenon_H67. % 19.63/19.88 (* end of lemma zenon_L17_ *) % 19.63/19.88 assert (zenon_L18_ : (~((e13) = (e13))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H6a. % 19.63/19.88 apply zenon_H6a. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L18_ *) % 19.63/19.88 assert (zenon_L19_ : (~((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H6b zenon_H15. % 19.63/19.88 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H6a]. % 19.63/19.88 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H6c. apply sym_equal. exact zenon_H15. % 19.63/19.88 apply zenon_H6a. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L19_ *) % 19.63/19.88 assert (zenon_L20_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> ((op1 (e10) (e13)) = (e12)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H6d zenon_H6e zenon_H6f zenon_H15. % 19.63/19.88 cut (((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H6d. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H6e. % 19.63/19.88 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 19.63/19.88 cut (((e12) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H70]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e12) = (op1 (e10) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H70. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H26. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H71]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H71 zenon_H6f). % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 apply (zenon_L19_); trivial. % 19.63/19.88 (* end of lemma zenon_L20_ *) % 19.63/19.88 assert (zenon_L21_ : (~((e23) = (e23))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H72. % 19.63/19.88 apply zenon_H72. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L21_ *) % 19.63/19.88 assert (zenon_L22_ : (~((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H73 zenon_H2e. % 19.63/19.88 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H53. apply sym_equal. exact zenon_H2e. % 19.63/19.88 apply zenon_H72. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L22_ *) % 19.63/19.88 assert (zenon_L23_ : (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op2 (e20) (e23)) = (e22)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H74 zenon_H67 zenon_H75 zenon_H2e. % 19.63/19.88 cut (((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H74. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H67. % 19.63/19.88 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 19.63/19.88 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H76]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e22) = (op2 (e20) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H76. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H3f. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H77]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H77 zenon_H75). % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 apply (zenon_L22_); trivial. % 19.63/19.88 (* end of lemma zenon_L23_ *) % 19.63/19.88 assert (zenon_L24_ : (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e10)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H78 zenon_H5e zenon_H79. % 19.63/19.88 cut (((op1 (e10) (e11)) = (e10)) = ((op1 (e10) (e11)) = (op1 (e10) (e12)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H78. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H5e. % 19.63/19.88 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H7a]. % 19.63/19.88 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H19]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H19. apply refl_equal. % 19.63/19.88 apply zenon_H7a. apply sym_equal. exact zenon_H79. % 19.63/19.88 (* end of lemma zenon_L24_ *) % 19.63/19.88 assert (zenon_L25_ : (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((op2 (e20) (e21)) = (e20)) -> ((op2 (e20) (e22)) = (e20)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H7b zenon_H56 zenon_H7c. % 19.63/19.88 cut (((op2 (e20) (e21)) = (e20)) = ((op2 (e20) (e21)) = (op2 (e20) (e22)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H7b. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H56. % 19.63/19.88 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 19.63/19.88 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H32]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H32. apply refl_equal. % 19.63/19.88 apply zenon_H7d. apply sym_equal. exact zenon_H7c. % 19.63/19.88 (* end of lemma zenon_L25_ *) % 19.63/19.88 assert (zenon_L26_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e20) (e23)) = (e20)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H7e zenon_H2c zenon_H7f. % 19.63/19.88 cut (((e20) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H7e. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2c. % 19.63/19.88 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 19.63/19.88 cut (((e20) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H3f | zenon_intro zenon_H40 ]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e20) = (op2 (e20) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H81. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H3f. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H40]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H82 zenon_H7f). % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 apply zenon_H40. apply refl_equal. % 19.63/19.88 apply zenon_H80. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L26_ *) % 19.63/19.88 assert (zenon_L27_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e10) (e13)) = (e10)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H83 zenon_H13 zenon_H84. % 19.63/19.88 cut (((e10) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H83. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H13. % 19.63/19.88 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 19.63/19.88 cut (((e10) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H86]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_H26 | zenon_intro zenon_H27 ]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e10) = (op1 (e10) (e13)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H86. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H26. % 19.63/19.88 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H27]. % 19.63/19.88 cut (((op1 (e10) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H87]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H87 zenon_H84). % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 apply zenon_H27. apply refl_equal. % 19.63/19.88 apply zenon_H85. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L27_ *) % 19.63/19.88 assert (zenon_L28_ : (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((op1 (e10) (e13)) = (e13)) -> ((op2 (e20) (e23)) = (e23)) -> ((h4 (e10)) = (op2 (e23) (e23))) -> ((e20) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H88 zenon_H89 zenon_H8a zenon_H4f zenon_H2c zenon_H8b. % 19.63/19.88 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H88. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H8b. % 19.63/19.88 cut (((e23) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H8c]. % 19.63/19.88 cut (((h4 (e13)) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H8d]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [ zenon_intro zenon_H8e | zenon_intro zenon_H8f ]. % 19.63/19.88 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13)))) = ((h4 (e13)) = (h4 (op1 (e10) (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H8d. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H8e. % 19.63/19.88 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 19.63/19.88 cut (((h4 (op1 (e10) (e13))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H90]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_H91 zenon_H89). % 19.63/19.88 apply zenon_H8f. apply refl_equal. % 19.63/19.88 apply zenon_H8f. apply refl_equal. % 19.63/19.88 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H92 | zenon_intro zenon_H93 ]. % 19.63/19.88 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((e23) = (op2 (h4 (e10)) (h4 (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H8c. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H92. % 19.63/19.88 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 19.63/19.88 cut (((op2 (h4 (e10)) (h4 (e13))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H94]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (h4 (e10)) (h4 (e13))) = (e23))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H94. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H8a. % 19.63/19.88 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 19.63/19.88 cut (((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H92 | zenon_intro zenon_H93 ]. % 19.63/19.88 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H95. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H92. % 19.63/19.88 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H93]. % 19.63/19.88 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H96]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 19.63/19.88 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.63/19.88 congruence. % 19.63/19.88 apply (zenon_L11_); trivial. % 19.63/19.88 exact (zenon_H97 zenon_H8b). % 19.63/19.88 apply zenon_H93. apply refl_equal. % 19.63/19.88 apply zenon_H93. apply refl_equal. % 19.63/19.88 apply zenon_H72. apply refl_equal. % 19.63/19.88 apply zenon_H93. apply refl_equal. % 19.63/19.88 apply zenon_H93. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L28_ *) % 19.63/19.88 assert (zenon_L29_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (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 (e23) (e23))) -> ((e20) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 19.63/19.88 do 0 intro. intros zenon_H98 zenon_H83 zenon_H25 zenon_H13 zenon_H15 zenon_H6e zenon_H6d zenon_H88 zenon_H8a zenon_H4f zenon_H2c zenon_H8b. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H98); [ zenon_intro zenon_H84 | zenon_intro zenon_H99 ]. % 19.63/19.88 apply (zenon_L27_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H99); [ zenon_intro zenon_H24 | zenon_intro zenon_H9a ]. % 19.63/19.88 apply (zenon_L4_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H9a); [ zenon_intro zenon_H6f | zenon_intro zenon_H89 ]. % 19.63/19.88 apply (zenon_L20_); trivial. % 19.63/19.88 apply (zenon_L28_); trivial. % 19.63/19.88 (* end of lemma zenon_L29_ *) % 19.63/19.88 assert (zenon_L30_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H9b zenon_H9c zenon_H30 zenon_H2e zenon_H2c zenon_H37 zenon_H3e zenon_H44. % 19.63/19.88 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.63/19.88 apply (zenon_L9_); trivial. % 19.63/19.88 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (e20) (e20)) = (op2 (e20) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_H30. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H9c. % 19.63/19.88 cut (((e20) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 19.63/19.88 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_H9e. apply refl_equal. % 19.63/19.88 apply zenon_H9d. apply sym_equal. exact zenon_H56. % 19.63/19.88 (* end of lemma zenon_L30_ *) % 19.63/19.88 assert (zenon_L31_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H2e zenon_H9f zenon_H2c zenon_Ha0. % 19.63/19.88 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 19.63/19.88 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Ha0. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Ha1. % 19.63/19.88 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 19.63/19.88 cut (((op2 (e23) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e23) (e20)) = (op2 (e20) (e20)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Ha3. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2e. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.63/19.88 cut (((e21) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 19.63/19.88 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e21) = (op2 (e23) (e20)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Ha4. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Ha1. % 19.63/19.88 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 19.63/19.88 cut (((op2 (e23) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_Ha5 zenon_H9f). % 19.63/19.88 apply zenon_Ha2. apply refl_equal. % 19.63/19.88 apply zenon_Ha2. apply refl_equal. % 19.63/19.88 apply (zenon_L5_); trivial. % 19.63/19.88 apply zenon_Ha2. apply refl_equal. % 19.63/19.88 apply zenon_Ha2. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L31_ *) % 19.63/19.88 assert (zenon_L32_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))) -> ((op2 (e20) (e20)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e21) (e21)) = (e21)) -> False). % 19.63/19.88 do 0 intro. intros zenon_Ha6 zenon_H47 zenon_H2c zenon_Ha7. % 19.63/19.88 cut (((op2 (e20) (e20)) = (e21)) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Ha6. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H47. % 19.63/19.88 cut (((e21) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 19.63/19.88 cut (((op2 (e20) (e20)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e20) (e20)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Ha9. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Haa. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.63/19.88 congruence. % 19.63/19.88 apply (zenon_L5_); trivial. % 19.63/19.88 apply zenon_Hab. apply refl_equal. % 19.63/19.88 apply zenon_Hab. apply refl_equal. % 19.63/19.88 apply zenon_Ha8. apply sym_equal. exact zenon_Ha7. % 19.63/19.88 (* end of lemma zenon_L32_ *) % 19.63/19.88 assert (zenon_L33_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e21) (e21)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> False). % 19.63/19.88 do 0 intro. intros zenon_H2e zenon_Hac zenon_H47 zenon_Ha7 zenon_H2c zenon_Had. % 19.63/19.88 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 19.63/19.88 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Had. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Hae. % 19.63/19.88 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 19.63/19.88 cut (((op2 (e23) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 19.63/19.88 congruence. % 19.63/19.88 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e23) (e21)) = (op2 (e21) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hb0. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2e. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 19.63/19.88 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hb1]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_Hae | zenon_intro zenon_Haf ]. % 19.63/19.88 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e21) = (op2 (e23) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hb1. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Hae. % 19.63/19.88 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 19.63/19.88 cut (((op2 (e23) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_Hb2 zenon_Hac). % 19.63/19.88 apply zenon_Haf. apply refl_equal. % 19.63/19.88 apply zenon_Haf. apply refl_equal. % 19.63/19.88 apply (zenon_L32_); trivial. % 19.63/19.88 apply zenon_Haf. apply refl_equal. % 19.63/19.88 apply zenon_Haf. apply refl_equal. % 19.63/19.88 (* end of lemma zenon_L33_ *) % 19.63/19.88 assert (zenon_L34_ : (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e21) (e23)) = (e21)) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hb3 zenon_Ha7 zenon_Hb4. % 19.63/19.88 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (e21) (e21)) = (op2 (e21) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hb3. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Ha7. % 19.63/19.88 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 19.63/19.88 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_Hb6. apply refl_equal. % 19.63/19.88 apply zenon_Hb5. apply sym_equal. exact zenon_Hb4. % 19.63/19.88 (* end of lemma zenon_L34_ *) % 19.63/19.88 assert (zenon_L35_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e23)))) -> ((op2 (e20) (e20)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hb7 zenon_H47 zenon_H2c zenon_Hb8. % 19.63/19.88 cut (((op2 (e20) (e20)) = (e21)) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e23)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hb7. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H47. % 19.63/19.88 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 19.63/19.88 cut (((op2 (e20) (e20)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Ha9]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e20) (e20)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Ha9. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Haa. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.63/19.88 congruence. % 19.63/19.88 apply (zenon_L5_); trivial. % 19.63/19.88 apply zenon_Hab. apply refl_equal. % 19.63/19.88 apply zenon_Hab. apply refl_equal. % 19.63/19.88 apply zenon_Hb9. apply sym_equal. exact zenon_Hb8. % 19.63/19.88 (* end of lemma zenon_L35_ *) % 19.63/19.88 assert (zenon_L36_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e23) (e22)))) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e23) (e22)) = (e21)) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hba zenon_H2c zenon_Hb8 zenon_H47 zenon_Hbb. % 19.63/19.88 cut (((op2 (e22) (e23)) = (e21)) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e23) (e22)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hba. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Hb8. % 19.63/19.88 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 19.63/19.88 cut (((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [ zenon_intro zenon_Haa | zenon_intro zenon_Hab ]. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e22) (e23)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hbd. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Haa. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_Hab]. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 19.63/19.88 congruence. % 19.63/19.88 apply (zenon_L35_); trivial. % 19.63/19.88 apply zenon_Hab. apply refl_equal. % 19.63/19.88 apply zenon_Hab. apply refl_equal. % 19.63/19.88 apply zenon_Hbc. apply sym_equal. exact zenon_Hbb. % 19.63/19.88 (* end of lemma zenon_L36_ *) % 19.63/19.88 assert (zenon_L37_ : (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e22)) = (e21)) -> ((op2 (e23) (e22)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hbe zenon_H2e zenon_Hbf zenon_Hbb zenon_H2c zenon_Hb8 zenon_H47. % 19.63/19.88 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e22) (e22)) = (op2 (e23) (e22)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hbe. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_H2e. % 19.63/19.88 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hba]. % 19.63/19.88 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hc0]. % 19.63/19.88 congruence. % 19.63/19.88 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hc2 ]. % 19.63/19.88 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e21) = (op2 (e22) (e22)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hc0. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Hc1. % 19.63/19.88 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 19.63/19.88 cut (((op2 (e22) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hc3]. % 19.63/19.88 congruence. % 19.63/19.88 exact (zenon_Hc3 zenon_Hbf). % 19.63/19.88 apply zenon_Hc2. apply refl_equal. % 19.63/19.88 apply zenon_Hc2. apply refl_equal. % 19.63/19.88 apply (zenon_L36_); trivial. % 19.63/19.88 (* end of lemma zenon_L37_ *) % 19.63/19.88 assert (zenon_L38_ : (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e22)) = (e20))) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e22) (e23)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e23) (e22)) = (e21)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e22)) = (e23))) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hc4 zenon_Hc5 zenon_H47 zenon_Hb8 zenon_H2c zenon_Hbb zenon_H2e zenon_Hbe zenon_Hc6 zenon_Hc7. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hc4); [ zenon_intro zenon_Hc9 | zenon_intro zenon_Hc8 ]. % 19.63/19.88 exact (zenon_Hc5 zenon_Hc9). % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hc8); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hca ]. % 19.63/19.88 apply (zenon_L37_); trivial. % 19.63/19.88 apply (zenon_or_s _ _ zenon_Hca); [ zenon_intro zenon_Hcc | zenon_intro zenon_Hcb ]. % 19.63/19.88 exact (zenon_Hc6 zenon_Hcc). % 19.63/19.88 exact (zenon_Hc7 zenon_Hcb). % 19.63/19.88 (* end of lemma zenon_L38_ *) % 19.63/19.88 assert (zenon_L39_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 19.63/19.88 do 0 intro. intros zenon_Hcd zenon_Hce zenon_Hcf. % 19.63/19.88 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))). % 19.63/19.88 intro zenon_D_pnotp. % 19.63/19.88 apply zenon_Hcd. % 19.63/19.88 rewrite <- zenon_D_pnotp. % 19.63/19.88 exact zenon_Hce. % 19.63/19.88 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hd0]. % 19.63/19.88 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 19.63/19.88 congruence. % 19.63/19.88 apply zenon_Ha2. apply refl_equal. % 19.63/19.88 apply zenon_Hd0. apply sym_equal. exact zenon_Hcf. % 19.63/19.88 (* end of lemma zenon_L39_ *) % 19.63/19.88 assert (zenon_L40_ : ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e23)) = (e22)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H67 zenon_Hd1 zenon_H2e zenon_Hd2. % 19.63/19.89 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd4 ]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hd2. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hd3. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((op2 (e22) (e23)) = (op2 (e21) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hd5. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H67. % 19.63/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 19.63/19.89 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd4 ]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e22) = (op2 (e22) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hd6. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hd3. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_Hd7]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_Hd7 zenon_Hd1). % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 apply (zenon_L22_); trivial. % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L40_ *) % 19.63/19.89 assert (zenon_L41_ : ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e22)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (e20))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hd8 zenon_H67 zenon_Hd2 zenon_H2c zenon_Hd9 zenon_Hcd zenon_Hda zenon_H3e zenon_Hb3 zenon_Hc4 zenon_Hc6 zenon_Hbe zenon_Hc5 zenon_Hdb zenon_Ha7 zenon_Had zenon_H2e zenon_Ha0 zenon_H30 zenon_H37 zenon_H44 zenon_Hdc. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hd8); [ zenon_intro zenon_Hc7 | zenon_intro zenon_Hd1 ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hce ]. % 19.63/19.89 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hd9); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hcf ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hda); [ zenon_intro zenon_H9f | zenon_intro zenon_Hde ]. % 19.63/19.89 apply (zenon_L31_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hde); [ zenon_intro zenon_Hac | zenon_intro zenon_Hdf ]. % 19.63/19.89 apply (zenon_L33_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hdf); [ zenon_intro zenon_Hbb | zenon_intro zenon_He0 ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H3d | zenon_intro zenon_He1 ]. % 19.63/19.89 apply (zenon_L8_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 19.63/19.89 apply (zenon_L34_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_He0 ]. % 19.63/19.89 apply (zenon_L38_); trivial. % 19.63/19.89 exact (zenon_Hdd zenon_He0). % 19.63/19.89 exact (zenon_Hdd zenon_He0). % 19.63/19.89 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H2f | zenon_intro zenon_H48 ]. % 19.63/19.89 apply (zenon_L6_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H36 | zenon_intro zenon_H3d ]. % 19.63/19.89 apply (zenon_L7_); trivial. % 19.63/19.89 apply (zenon_L8_); trivial. % 19.63/19.89 apply (zenon_L39_); trivial. % 19.63/19.89 apply (zenon_L40_); trivial. % 19.63/19.89 (* end of lemma zenon_L41_ *) % 19.63/19.89 assert (zenon_L42_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hcc zenon_He3 zenon_He4. % 19.63/19.89 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_Hc1 | zenon_intro zenon_Hc2 ]. % 19.63/19.89 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_He4. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hc1. % 19.63/19.89 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 19.63/19.89 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_He5]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_He5. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hcc. % 19.63/19.89 cut (((e22) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 19.63/19.89 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_Hc2]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_Hc2. apply refl_equal. % 19.63/19.89 apply zenon_He6. apply sym_equal. exact zenon_He3. % 19.63/19.89 apply zenon_Hc2. apply refl_equal. % 19.63/19.89 apply zenon_Hc2. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L42_ *) % 19.63/19.89 assert (zenon_L43_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H9b zenon_He7 zenon_H67 zenon_H74 zenon_Hcc zenon_He4 zenon_H58 zenon_H7b zenon_He8 zenon_H30 zenon_H2e zenon_H2c zenon_H37 zenon_H3e zenon_H44. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.63/19.89 apply (zenon_L9_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_He9 | zenon_intro zenon_H7c ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 19.63/19.89 exact (zenon_He9 zenon_Heb). % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Hec ]. % 19.63/19.89 apply (zenon_L14_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_He3 | zenon_intro zenon_H75 ]. % 19.63/19.89 apply (zenon_L42_); trivial. % 19.63/19.89 apply (zenon_L23_); trivial. % 19.63/19.89 apply (zenon_L25_); trivial. % 19.63/19.89 (* end of lemma zenon_L43_ *) % 19.63/19.89 assert (zenon_L44_ : ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e22)))) -> (~((e20) = (e22))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e21) (e21)) = (e21)) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e22) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e23) (e20)) = (e21))\/(((op2 (e23) (e21)) = (e21))\/(((op2 (e23) (e22)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hed zenon_He8 zenon_H7b zenon_H58 zenon_He4 zenon_H74 zenon_He7 zenon_H9b zenon_Hdc zenon_H44 zenon_H37 zenon_H30 zenon_Ha0 zenon_H2e zenon_Had zenon_Ha7 zenon_Hdb zenon_Hc5 zenon_Hbe zenon_Hc4 zenon_Hb3 zenon_H3e zenon_Hda zenon_Hcd zenon_Hd9 zenon_H2c zenon_Hd2 zenon_H67 zenon_Hd8. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hed); [ zenon_intro zenon_Hc6 | zenon_intro zenon_Hcc ]. % 19.63/19.89 apply (zenon_L41_); trivial. % 19.63/19.89 apply (zenon_L43_); trivial. % 19.63/19.89 (* end of lemma zenon_L44_ *) % 19.63/19.89 assert (zenon_L45_ : ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hee zenon_Hef zenon_H17 zenon_H15 zenon_H13 zenon_H1e zenon_H25 zenon_H49. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.63/19.89 apply (zenon_L10_); trivial. % 19.63/19.89 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e10) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H17. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hef. % 19.63/19.89 cut (((e10) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 19.63/19.89 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hf1]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_Hf1. apply refl_equal. % 19.63/19.89 apply zenon_Hf0. apply sym_equal. exact zenon_H5e. % 19.63/19.89 (* end of lemma zenon_L45_ *) % 19.63/19.89 assert (zenon_L46_ : (~((e12) = (e12))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H62. % 19.63/19.89 apply zenon_H62. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L46_ *) % 19.63/19.89 assert (zenon_L47_ : (~((e10) = (e12))) -> ((op1 (e12) (e10)) = (e12)) -> ((op1 (e12) (e10)) = (e10)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H60 zenon_Hf2 zenon_Hf3. % 19.63/19.89 cut (((op1 (e12) (e10)) = (e12)) = ((e10) = (e12))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H60. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hf2. % 19.63/19.89 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H62]. % 19.63/19.89 cut (((op1 (e12) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Hf4]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_Hf4 zenon_Hf3). % 19.63/19.89 apply zenon_H62. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L47_ *) % 19.63/19.89 assert (zenon_L48_ : (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e10)) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hf5 zenon_H13 zenon_Hf6. % 19.63/19.89 cut (((e10) = (op1 (e13) (e13))) = ((op1 (e13) (e11)) = (op1 (e13) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hf5. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H13. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 19.63/19.89 cut (((e10) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Hf8 | zenon_intro zenon_Hf9 ]. % 19.63/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e10) = (op1 (e13) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hf7. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hf8. % 19.63/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 19.63/19.89 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Hfa]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_Hfa zenon_Hf6). % 19.63/19.89 apply zenon_Hf9. apply refl_equal. % 19.63/19.89 apply zenon_Hf9. apply refl_equal. % 19.63/19.89 apply zenon_H85. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L48_ *) % 19.63/19.89 assert (zenon_L49_ : (~((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))) -> ((op1 (e10) (e10)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e11) (e11)) = (e11)) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hfb zenon_H4c zenon_H13 zenon_Hfc. % 19.63/19.89 cut (((op1 (e10) (e10)) = (e11)) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hfb. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H4c. % 19.63/19.89 cut (((e11) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 19.63/19.89 cut (((op1 (e10) (e10)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_Hfe]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [ zenon_intro zenon_Hff | zenon_intro zenon_H100 ]. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e10) (e10)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hfe. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hff. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H100]. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 19.63/19.89 congruence. % 19.63/19.89 apply (zenon_L1_); trivial. % 19.63/19.89 apply zenon_H100. apply refl_equal. % 19.63/19.89 apply zenon_H100. apply refl_equal. % 19.63/19.89 apply zenon_Hfd. apply sym_equal. exact zenon_Hfc. % 19.63/19.89 (* end of lemma zenon_L49_ *) % 19.63/19.89 assert (zenon_L50_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e11)) -> ((op1 (e10) (e10)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H15 zenon_H101 zenon_H4c zenon_Hfc zenon_H13 zenon_H102. % 19.63/19.89 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Hf8 | zenon_intro zenon_Hf9 ]. % 19.63/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H102. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hf8. % 19.63/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 19.63/19.89 cut (((op1 (e13) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H103]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e13) (e11)) = (op1 (e11) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H103. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H15. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 19.63/19.89 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H104]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Hf8 | zenon_intro zenon_Hf9 ]. % 19.63/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e11) = (op1 (e13) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H104. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hf8. % 19.63/19.89 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf9]. % 19.63/19.89 cut (((op1 (e13) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H105 zenon_H101). % 19.63/19.89 apply zenon_Hf9. apply refl_equal. % 19.63/19.89 apply zenon_Hf9. apply refl_equal. % 19.63/19.89 apply (zenon_L49_); trivial. % 19.63/19.89 apply zenon_Hf9. apply refl_equal. % 19.63/19.89 apply zenon_Hf9. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L50_ *) % 19.63/19.89 assert (zenon_L51_ : (~((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e13)) = (e12)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e12)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H106 zenon_H107 zenon_H15 zenon_H108. % 19.63/19.89 cut (((op1 (e11) (e13)) = (e12)) = ((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e13) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H106. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H107. % 19.63/19.89 cut (((e12) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 19.63/19.89 cut (((op1 (e11) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H10c ]. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) = ((op1 (e11) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H10a. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H10b. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 19.63/19.89 congruence. % 19.63/19.89 apply (zenon_L19_); trivial. % 19.63/19.89 apply zenon_H10c. apply refl_equal. % 19.63/19.89 apply zenon_H10c. apply refl_equal. % 19.63/19.89 apply zenon_H109. apply sym_equal. exact zenon_H108. % 19.63/19.89 (* end of lemma zenon_L51_ *) % 19.63/19.89 assert (zenon_L52_ : (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e11) (e13)) = (e12)) -> ((op1 (e13) (e11)) = (e12)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H10d zenon_H6e zenon_H10e zenon_H107 zenon_H108 zenon_H15. % 19.63/19.89 cut (((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) = ((op1 (e12) (e11)) = (op1 (e13) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H10d. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H6e. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H106]. % 19.63/19.89 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 19.63/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e12) = (op1 (e12) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H10f. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H110. % 19.63/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 19.63/19.89 cut (((op1 (e12) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H112 zenon_H10e). % 19.63/19.89 apply zenon_H111. apply refl_equal. % 19.63/19.89 apply zenon_H111. apply refl_equal. % 19.63/19.89 apply (zenon_L51_); trivial. % 19.63/19.89 (* end of lemma zenon_L52_ *) % 19.63/19.89 assert (zenon_L53_ : (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H113 zenon_H114 zenon_H115. % 19.63/19.89 cut (((op1 (e13) (e10)) = (e13)) = ((op1 (e13) (e10)) = (op1 (e13) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H113. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H114. % 19.63/19.89 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 19.63/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H117. apply refl_equal. % 19.63/19.89 apply zenon_H116. apply sym_equal. exact zenon_H115. % 19.63/19.89 (* end of lemma zenon_L53_ *) % 19.63/19.89 assert (zenon_L54_ : (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e10) (e10)) = (e11)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e12)) -> ((op1 (e12) (e11)) = (e12)) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H118 zenon_Hf5 zenon_H102 zenon_H13 zenon_Hfc zenon_H4c zenon_H15 zenon_H107 zenon_H10e zenon_H6e zenon_H10d zenon_H113 zenon_H114. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H119 ]. % 19.63/19.89 apply (zenon_L48_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H101 | zenon_intro zenon_H11a ]. % 19.63/19.89 apply (zenon_L50_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H108 | zenon_intro zenon_H115 ]. % 19.63/19.89 apply (zenon_L52_); trivial. % 19.63/19.89 apply (zenon_L53_); trivial. % 19.63/19.89 (* end of lemma zenon_L54_ *) % 19.63/19.89 assert (zenon_L55_ : ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> ((op1 (e12) (e13)) = (e12)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H6e zenon_H11b zenon_H15 zenon_H11c. % 19.63/19.89 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H11d | zenon_intro zenon_H11e ]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e11) (e13)) = (op1 (e12) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H11c. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H11d. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) = ((op1 (e12) (e13)) = (op1 (e11) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H11f. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H6e. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 19.63/19.89 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H120]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H11d | zenon_intro zenon_H11e ]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e12) = (op1 (e12) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H120. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H11d. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H121 zenon_H11b). % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply (zenon_L19_); trivial. % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L55_ *) % 19.63/19.89 assert (zenon_L56_ : (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e10) (e10)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e13) (e13)) = (e12))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H122 zenon_H6d zenon_H114 zenon_H113 zenon_H10d zenon_H10e zenon_H4c zenon_Hfc zenon_H13 zenon_H102 zenon_Hf5 zenon_H118 zenon_H11c zenon_H15 zenon_H6e zenon_H123. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H6f | zenon_intro zenon_H124 ]. % 19.63/19.89 apply (zenon_L20_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H107 | zenon_intro zenon_H125 ]. % 19.63/19.89 apply (zenon_L54_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H11b | zenon_intro zenon_H126 ]. % 19.63/19.89 apply (zenon_L55_); trivial. % 19.63/19.89 exact (zenon_H123 zenon_H126). % 19.63/19.89 (* end of lemma zenon_L56_ *) % 19.63/19.89 assert (zenon_L57_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e12)) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e13)) = (e12))) -> (~((e10) = (e12))) -> ((op1 (e12) (e10)) = (e10)) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H49 zenon_H11c zenon_H6e zenon_H127 zenon_H122 zenon_H6d zenon_H114 zenon_H113 zenon_H10d zenon_Hfc zenon_H102 zenon_Hf5 zenon_H118 zenon_H123 zenon_H60 zenon_Hf3 zenon_H128 zenon_H17 zenon_H1e zenon_H15 zenon_H13 zenon_H25. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H129 ]. % 19.63/19.89 apply (zenon_L47_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10e | zenon_intro zenon_H12a ]. % 19.63/19.89 apply (zenon_L56_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H12b | zenon_intro zenon_H11b ]. % 19.63/19.89 exact (zenon_H127 zenon_H12b). % 19.63/19.89 apply (zenon_L55_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H16 | zenon_intro zenon_H4d ]. % 19.63/19.89 apply (zenon_L2_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H1d | zenon_intro zenon_H24 ]. % 19.63/19.89 apply (zenon_L3_); trivial. % 19.63/19.89 apply (zenon_L4_); trivial. % 19.63/19.89 (* end of lemma zenon_L57_ *) % 19.63/19.89 assert (zenon_L58_ : ((e10) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e10)) -> (~((op1 (e13) (e13)) = (op1 (e11) (e10)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H13 zenon_H12c zenon_H12d. % 19.63/19.89 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H12e | zenon_intro zenon_H12f ]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((op1 (e13) (e13)) = (op1 (e11) (e10)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H12d. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H12e. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e10) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H130. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H13. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 19.63/19.89 cut (((e10) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H131]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H12e | zenon_intro zenon_H12f ]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e10) = (op1 (e11) (e10)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H131. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H12e. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H132 zenon_H12c). % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 apply zenon_H85. apply refl_equal. % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L58_ *) % 19.63/19.89 assert (zenon_L59_ : (~((op1 (e13) (e13)) = (op1 (e10) (e11)))) -> ((op1 (e11) (e10)) = (e10)) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e10) (e11)) = (e10)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H133 zenon_H12c zenon_H13 zenon_H5e. % 19.63/19.89 cut (((op1 (e11) (e10)) = (e10)) = ((op1 (e13) (e13)) = (op1 (e10) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H133. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H12c. % 19.63/19.89 cut (((e10) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf0]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H130]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_H134 | zenon_intro zenon_H85 ]. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H130. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H134. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 19.63/19.89 congruence. % 19.63/19.89 apply (zenon_L58_); trivial. % 19.63/19.89 apply zenon_H85. apply refl_equal. % 19.63/19.89 apply zenon_H85. apply refl_equal. % 19.63/19.89 apply zenon_Hf0. apply sym_equal. exact zenon_H5e. % 19.63/19.89 (* end of lemma zenon_L59_ *) % 19.63/19.89 assert (zenon_L60_ : ((op1 (e12) (e11)) = (e10)) -> ((op1 (e10) (e11)) = (e10)) -> ((op1 (e11) (e10)) = (e10)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H135 zenon_H5e zenon_H12c zenon_H13 zenon_H136. % 19.63/19.89 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 19.63/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e10) (e11)) = (op1 (e12) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H136. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H110. % 19.63/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 19.63/19.89 cut (((op1 (e12) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e10) = (op1 (e13) (e13))) = ((op1 (e12) (e11)) = (op1 (e10) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H137. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H13. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H133]. % 19.63/19.89 cut (((e10) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H138]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 19.63/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e10) = (op1 (e12) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H138. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H110. % 19.63/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 19.63/19.89 cut (((op1 (e12) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H139]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H139 zenon_H135). % 19.63/19.89 apply zenon_H111. apply refl_equal. % 19.63/19.89 apply zenon_H111. apply refl_equal. % 19.63/19.89 apply (zenon_L59_); trivial. % 19.63/19.89 apply zenon_H111. apply refl_equal. % 19.63/19.89 apply zenon_H111. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L60_ *) % 19.63/19.89 assert (zenon_L61_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e12) (e13)) = (e10)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H13a zenon_H13 zenon_H13b. % 19.63/19.89 cut (((e10) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H13a. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H13. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 19.63/19.89 cut (((e10) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H13c]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H11d | zenon_intro zenon_H11e ]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e10) = (op1 (e12) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H13c. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H11d. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H13d]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H13d zenon_H13b). % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply zenon_H85. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L61_ *) % 19.63/19.89 assert (zenon_L62_ : (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e13) (e10)) = (e10)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H13e zenon_H13 zenon_H13f. % 19.63/19.89 cut (((e10) = (op1 (e13) (e13))) = ((op1 (e13) (e10)) = (op1 (e13) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H13e. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H13. % 19.63/19.89 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 19.63/19.89 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H140]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H141 | zenon_intro zenon_H117 ]. % 19.63/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e10) = (op1 (e13) (e10)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H140. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H141. % 19.63/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 19.63/19.89 cut (((op1 (e13) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H142 zenon_H13f). % 19.63/19.89 apply zenon_H117. apply refl_equal. % 19.63/19.89 apply zenon_H117. apply refl_equal. % 19.63/19.89 apply zenon_H85. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L62_ *) % 19.63/19.89 assert (zenon_L63_ : (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H143 zenon_H114 zenon_H144. % 19.63/19.89 cut (((op1 (e13) (e10)) = (e13)) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H143. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H114. % 19.63/19.89 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H145]. % 19.63/19.89 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H117. apply refl_equal. % 19.63/19.89 apply zenon_H145. apply sym_equal. exact zenon_H144. % 19.63/19.89 (* end of lemma zenon_L63_ *) % 19.63/19.89 assert (zenon_L64_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H12b zenon_H146 zenon_H147. % 19.63/19.89 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_H148 | zenon_intro zenon_H149 ]. % 19.63/19.89 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H147. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H148. % 19.63/19.89 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 19.63/19.89 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H14a. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H12b. % 19.63/19.89 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 19.63/19.89 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H149]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H149. apply refl_equal. % 19.63/19.89 apply zenon_H14b. apply sym_equal. exact zenon_H146. % 19.63/19.89 apply zenon_H149. apply refl_equal. % 19.63/19.89 apply zenon_H149. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L64_ *) % 19.63/19.89 assert (zenon_L65_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((e10) = (e12))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H14c zenon_H14d zenon_H60 zenon_H5e zenon_H147 zenon_H12b zenon_H6d zenon_H6e zenon_H15. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H14f | zenon_intro zenon_H14e ]. % 19.63/19.89 exact (zenon_H14d zenon_H14f). % 19.63/19.89 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H5f | zenon_intro zenon_H150 ]. % 19.63/19.89 apply (zenon_L16_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H146 | zenon_intro zenon_H6f ]. % 19.63/19.89 apply (zenon_L64_); trivial. % 19.63/19.89 apply (zenon_L20_); trivial. % 19.63/19.89 (* end of lemma zenon_L65_ *) % 19.63/19.89 assert (zenon_L66_ : ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hee zenon_H14c zenon_H6e zenon_H6d zenon_H12b zenon_H147 zenon_H60 zenon_H78 zenon_H151 zenon_H17 zenon_H15 zenon_H13 zenon_H1e zenon_H25 zenon_H49. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.63/19.89 apply (zenon_L10_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H14d | zenon_intro zenon_H79 ]. % 19.63/19.89 apply (zenon_L65_); trivial. % 19.63/19.89 apply (zenon_L24_); trivial. % 19.63/19.89 (* end of lemma zenon_L66_ *) % 19.63/19.89 assert (zenon_L67_ : ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e11)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((e10) = (op1 (e13) (e13))) -> ((~((op1 (e13) (e13)) = (e12)))\/((op1 (e13) (e12)) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (e10))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((e10) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((~((op1 (e13) (e13)) = (e10)))\/((op1 (e13) (e10)) = (e13))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H152 zenon_H151 zenon_H78 zenon_H147 zenon_H14c zenon_Hee zenon_H13 zenon_H153 zenon_H143 zenon_H154 zenon_H155 zenon_H13a zenon_H156 zenon_H5e zenon_H136 zenon_H128 zenon_H6d zenon_H6e zenon_H15 zenon_H118 zenon_H113 zenon_H10d zenon_Hfc zenon_H102 zenon_Hf5 zenon_H11c zenon_H122 zenon_H60 zenon_H17 zenon_H1e zenon_H25 zenon_H49 zenon_H13e zenon_H157 zenon_H158. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H127 | zenon_intro zenon_H12b ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.63/19.89 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H123 | zenon_intro zenon_H144 ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hef | zenon_intro zenon_H159 ]. % 19.63/19.89 exact (zenon_H154 zenon_Hef). % 19.63/19.89 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H12c | zenon_intro zenon_H15a ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H155); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H15b ]. % 19.63/19.89 apply (zenon_L57_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H15b); [ zenon_intro zenon_H135 | zenon_intro zenon_H15c ]. % 19.63/19.89 apply (zenon_L60_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H15c); [ zenon_intro zenon_H15d | zenon_intro zenon_H13b ]. % 19.63/19.89 exact (zenon_H156 zenon_H15d). % 19.63/19.89 apply (zenon_L61_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H13f ]. % 19.63/19.89 apply (zenon_L57_); trivial. % 19.63/19.89 apply (zenon_L62_); trivial. % 19.63/19.89 apply (zenon_L63_); trivial. % 19.63/19.89 apply (zenon_L66_); trivial. % 19.63/19.89 (* end of lemma zenon_L67_ *) % 19.63/19.89 assert (zenon_L68_ : (~((e22) = (e22))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H5a. % 19.63/19.89 apply zenon_H5a. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L68_ *) % 19.63/19.89 assert (zenon_L69_ : (~((e20) = (e22))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e22) (e20)) = (e20)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H58 zenon_H15e zenon_H15f. % 19.63/19.89 cut (((op2 (e22) (e20)) = (e22)) = ((e20) = (e22))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H58. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H15e. % 19.63/19.89 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5a]. % 19.63/19.89 cut (((op2 (e22) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H160]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H160 zenon_H15f). % 19.63/19.89 apply zenon_H5a. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L69_ *) % 19.63/19.89 assert (zenon_L70_ : (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e23) (e20)) = (e20)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H161 zenon_H2c zenon_H162. % 19.63/19.89 cut (((e20) = (op2 (e23) (e23))) = ((op2 (e23) (e20)) = (op2 (e23) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H161. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H2c. % 19.63/19.89 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 19.63/19.89 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H163]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e23) (e20)) = (op2 (e23) (e20)))); [ zenon_intro zenon_Ha1 | zenon_intro zenon_Ha2 ]. % 19.63/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20))) = ((e20) = (op2 (e23) (e20)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H163. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Ha1. % 19.63/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 19.63/19.89 cut (((op2 (e23) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H164]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H164 zenon_H162). % 19.63/19.89 apply zenon_Ha2. apply refl_equal. % 19.63/19.89 apply zenon_Ha2. apply refl_equal. % 19.63/19.89 apply zenon_H80. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L70_ *) % 19.63/19.89 assert (zenon_L71_ : (~((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H165 zenon_H166 zenon_H13. % 19.63/19.89 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H167]. % 19.63/19.89 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.63/19.89 exact (zenon_H167 zenon_H166). % 19.63/19.89 (* end of lemma zenon_L71_ *) % 19.63/19.89 assert (zenon_L72_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e11)) -> ((op1 (e13) (e13)) = (e13)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H15 zenon_H168 zenon_H166 zenon_H13 zenon_H6d. % 19.63/19.89 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H169 | zenon_intro zenon_H16a ]. % 19.63/19.89 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H6d. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H169. % 19.63/19.89 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 19.63/19.89 cut (((op1 (e11) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16b]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e11) (e13)) = (op1 (e10) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H16b. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H15. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 19.63/19.89 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H169 | zenon_intro zenon_H16a ]. % 19.63/19.89 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e11) = (op1 (e11) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H16c. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H169. % 19.63/19.89 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 19.63/19.89 cut (((op1 (e11) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H16d zenon_H168). % 19.63/19.89 apply zenon_H16a. apply refl_equal. % 19.63/19.89 apply zenon_H16a. apply refl_equal. % 19.63/19.89 apply (zenon_L71_); trivial. % 19.63/19.89 apply zenon_H16a. apply refl_equal. % 19.63/19.89 apply zenon_H16a. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L72_ *) % 19.63/19.89 assert (zenon_L73_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e11)) -> ((op1 (e13) (e13)) = (e13)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H15 zenon_H16e zenon_H166 zenon_H13 zenon_H16f. % 19.63/19.89 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H11d | zenon_intro zenon_H11e ]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e10) (e13)) = (op1 (e12) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H16f. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H11d. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e12) (e13)) = (op1 (e10) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H170. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H15. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H165]. % 19.63/19.89 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H171]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_H11d | zenon_intro zenon_H11e ]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e11) = (op1 (e12) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H171. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H11d. % 19.63/19.89 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H11e]. % 19.63/19.89 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H172 zenon_H16e). % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply (zenon_L71_); trivial. % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 apply zenon_H11e. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L73_ *) % 19.63/19.89 assert (zenon_L74_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e13) (e13)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H15 zenon_Hfc zenon_H173 zenon_H13 zenon_H174. % 19.63/19.89 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H176 ]. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((op1 (e10) (e11)) = (op1 (e11) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H174. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H175. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H177]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e11) (e11)) = (op1 (e10) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H177. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H15. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H178]. % 19.63/19.89 cut (((e11) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hfd]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H176 ]. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e11) = (op1 (e11) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hfd. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H175. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 19.63/19.89 cut (((op1 (e11) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H179 zenon_Hfc). % 19.63/19.89 apply zenon_H176. apply refl_equal. % 19.63/19.89 apply zenon_H176. apply refl_equal. % 19.63/19.89 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 19.63/19.89 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.63/19.89 exact (zenon_H17a zenon_H173). % 19.63/19.89 apply zenon_H176. apply refl_equal. % 19.63/19.89 apply zenon_H176. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L74_ *) % 19.63/19.89 assert (zenon_L75_ : (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H17b zenon_H25 zenon_H6d zenon_H16f zenon_H166 zenon_H15 zenon_Hfc zenon_H13 zenon_H174. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H24 | zenon_intro zenon_H17c ]. % 19.63/19.89 apply (zenon_L4_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H168 | zenon_intro zenon_H17d ]. % 19.63/19.89 apply (zenon_L72_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H16e | zenon_intro zenon_H173 ]. % 19.63/19.89 apply (zenon_L73_); trivial. % 19.63/19.89 apply (zenon_L74_); trivial. % 19.63/19.89 (* end of lemma zenon_L75_ *) % 19.63/19.89 assert (zenon_L76_ : ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (e10))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e13) (e13)) = (e13)) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H17e zenon_H25 zenon_H16f zenon_H174 zenon_H17b zenon_H17f zenon_H15 zenon_H6e zenon_H180 zenon_H181 zenon_H6d zenon_H13 zenon_H166 zenon_H182. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H17e); [ zenon_intro zenon_H179 | zenon_intro zenon_Hfc ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H182); [ zenon_intro zenon_H183 | zenon_intro zenon_H168 ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H17f); [ zenon_intro zenon_H185 | zenon_intro zenon_H184 ]. % 19.63/19.89 exact (zenon_H181 zenon_H185). % 19.63/19.89 apply (zenon_or_s _ _ zenon_H184); [ zenon_intro zenon_Hfc | zenon_intro zenon_H186 ]. % 19.63/19.89 exact (zenon_H179 zenon_Hfc). % 19.63/19.89 apply (zenon_or_s _ _ zenon_H186); [ zenon_intro zenon_H188 | zenon_intro zenon_H187 ]. % 19.63/19.89 cut (((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) = ((op1 (e11) (e11)) = (op1 (e11) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H180. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H6e. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 19.63/19.89 cut (((e12) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e11) (e11)) = (op1 (e11) (e11)))); [ zenon_intro zenon_H175 | zenon_intro zenon_H176 ]. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e11) (e11))) = ((e12) = (op1 (e11) (e11)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H189. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H175. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 19.63/19.89 cut (((op1 (e11) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H18a]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H18a zenon_H188). % 19.63/19.89 apply zenon_H176. apply refl_equal. % 19.63/19.89 apply zenon_H176. apply refl_equal. % 19.63/19.89 apply (zenon_L19_); trivial. % 19.63/19.89 exact (zenon_H183 zenon_H187). % 19.63/19.89 apply (zenon_L72_); trivial. % 19.63/19.89 apply (zenon_L75_); trivial. % 19.63/19.89 (* end of lemma zenon_L76_ *) % 19.63/19.89 assert (zenon_L77_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e10)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H15 zenon_H18b zenon_H13 zenon_H18c. % 19.63/19.89 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H12e | zenon_intro zenon_H12f ]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((op1 (e10) (e10)) = (op1 (e11) (e10)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H18c. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H12e. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H18d]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e11) (e10)) = (op1 (e10) (e10)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H18d. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H15. % 19.63/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 19.63/19.89 cut (((e11) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H18e]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_H12e | zenon_intro zenon_H12f ]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e11) = (op1 (e11) (e10)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H18e. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H12e. % 19.63/19.89 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 19.63/19.89 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H18f]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H18f zenon_H18b). % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 apply (zenon_L1_); trivial. % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 apply zenon_H12f. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L77_ *) % 19.63/19.89 assert (zenon_L78_ : ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e11) (e10)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((op1 (e13) (e13)) = (e13)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e12) (e13)) = (e11))\/((op1 (e13) (e13)) = (e11))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H190 zenon_H18c zenon_H182 zenon_H166 zenon_H13 zenon_H6d zenon_H180 zenon_H6e zenon_H15 zenon_H17f zenon_H17b zenon_H174 zenon_H16f zenon_H25 zenon_H17e. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H190); [ zenon_intro zenon_H181 | zenon_intro zenon_H18b ]. % 19.63/19.89 apply (zenon_L76_); trivial. % 19.63/19.89 apply (zenon_L77_); trivial. % 19.63/19.89 (* end of lemma zenon_L78_ *) % 19.63/19.89 assert (zenon_L79_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e23)))) -> ((op2 (e23) (e23)) = (e23)) -> ((e20) = (op2 (e23) (e23))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H191 zenon_H192 zenon_H2c. % 19.63/19.89 cut (((op2 (e23) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 19.63/19.89 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.63/19.89 exact (zenon_H193 zenon_H192). % 19.63/19.89 (* end of lemma zenon_L79_ *) % 19.63/19.89 assert (zenon_L80_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e21)) -> ((op2 (e23) (e23)) = (e23)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H2e zenon_Hb4 zenon_H192 zenon_H2c zenon_H74. % 19.63/19.89 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H195 ]. % 19.63/19.89 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H74. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H194. % 19.63/19.89 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 19.63/19.89 cut (((op2 (e21) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e21) (e23)) = (op2 (e20) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H196. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H2e. % 19.63/19.89 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 19.63/19.89 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H194 | zenon_intro zenon_H195 ]. % 19.63/19.89 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e21) = (op2 (e21) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hb5. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H194. % 19.63/19.89 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H195]. % 19.63/19.89 cut (((op2 (e21) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H197 zenon_Hb4). % 19.63/19.89 apply zenon_H195. apply refl_equal. % 19.63/19.89 apply zenon_H195. apply refl_equal. % 19.63/19.89 apply (zenon_L79_); trivial. % 19.63/19.89 apply zenon_H195. apply refl_equal. % 19.63/19.89 apply zenon_H195. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L80_ *) % 19.63/19.89 assert (zenon_L81_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e21)) -> ((op2 (e23) (e23)) = (e23)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H2e zenon_Hb8 zenon_H192 zenon_H2c zenon_H198. % 19.63/19.89 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd4 ]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H198. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hd3. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H199]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e22) (e23)) = (op2 (e20) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H199. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H2e. % 19.63/19.89 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H191]. % 19.63/19.89 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hb9]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd4 ]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e21) = (op2 (e22) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hb9. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hd3. % 19.63/19.89 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 19.63/19.89 cut (((op2 (e22) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H19a zenon_Hb8). % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 apply (zenon_L79_); trivial. % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 apply zenon_Hd4. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L81_ *) % 19.63/19.89 assert (zenon_L82_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e23) (e23)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H2e zenon_Ha7 zenon_He0 zenon_H2c zenon_H19b. % 19.63/19.89 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H19c | zenon_intro zenon_Hb6 ]. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((op2 (e20) (e21)) = (op2 (e21) (e21)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H19b. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H19c. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H19d]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e21) (e21)) = (op2 (e20) (e21)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H19d. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H2e. % 19.63/19.89 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H19e]. % 19.63/19.89 cut (((e21) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H19c | zenon_intro zenon_Hb6 ]. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e21) = (op2 (e21) (e21)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Ha8. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H19c. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 19.63/19.89 cut (((op2 (e21) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H19f]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H19f zenon_Ha7). % 19.63/19.89 apply zenon_Hb6. apply refl_equal. % 19.63/19.89 apply zenon_Hb6. apply refl_equal. % 19.63/19.89 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_Hdd]. % 19.63/19.89 cut (((op2 (e23) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.63/19.89 exact (zenon_Hdd zenon_He0). % 19.63/19.89 apply zenon_Hb6. apply refl_equal. % 19.63/19.89 apply zenon_Hb6. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L82_ *) % 19.63/19.89 assert (zenon_L83_ : (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e23) (e23)) = (e23)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e21)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_Hdb zenon_H3e zenon_H74 zenon_H198 zenon_H192 zenon_H2e zenon_Ha7 zenon_H2c zenon_H19b. % 19.63/19.89 apply (zenon_or_s _ _ zenon_Hdb); [ zenon_intro zenon_H3d | zenon_intro zenon_He1 ]. % 19.63/19.89 apply (zenon_L8_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_He1); [ zenon_intro zenon_Hb4 | zenon_intro zenon_He2 ]. % 19.63/19.89 apply (zenon_L80_); trivial. % 19.63/19.89 apply (zenon_or_s _ _ zenon_He2); [ zenon_intro zenon_Hb8 | zenon_intro zenon_He0 ]. % 19.63/19.89 apply (zenon_L81_); trivial. % 19.63/19.89 apply (zenon_L82_); trivial. % 19.63/19.89 (* end of lemma zenon_L83_ *) % 19.63/19.89 assert (zenon_L84_ : ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e21)) = (e20))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e23) (e23)) = (e23)) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1a0 zenon_H3e zenon_H198 zenon_H19b zenon_Hdb zenon_H1a1 zenon_H2e zenon_H67 zenon_Hb3 zenon_H1a2 zenon_H74 zenon_H2c zenon_H192 zenon_H1a3. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H1a0); [ zenon_intro zenon_H19f | zenon_intro zenon_Ha7 ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H1a3); [ zenon_intro zenon_H1a4 | zenon_intro zenon_Hb4 ]. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H1a1); [ zenon_intro zenon_H1a6 | zenon_intro zenon_H1a5 ]. % 19.63/19.89 exact (zenon_H1a2 zenon_H1a6). % 19.63/19.89 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H1a7 ]. % 19.63/19.89 exact (zenon_H19f zenon_Ha7). % 19.63/19.89 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H1a8 ]. % 19.63/19.89 cut (((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((op2 (e21) (e21)) = (op2 (e21) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_Hb3. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H67. % 19.63/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 19.63/19.89 cut (((e22) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1aa]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e21) (e21)) = (op2 (e21) (e21)))); [ zenon_intro zenon_H19c | zenon_intro zenon_Hb6 ]. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e21) (e21))) = ((e22) = (op2 (e21) (e21)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1aa. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H19c. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 19.63/19.89 cut (((op2 (e21) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H1ab zenon_H1a9). % 19.63/19.89 apply zenon_Hb6. apply refl_equal. % 19.63/19.89 apply zenon_Hb6. apply refl_equal. % 19.63/19.89 apply (zenon_L22_); trivial. % 19.63/19.89 exact (zenon_H1a4 zenon_H1a8). % 19.63/19.89 apply (zenon_L80_); trivial. % 19.63/19.89 apply (zenon_L83_); trivial. % 19.63/19.89 (* end of lemma zenon_L84_ *) % 19.63/19.89 assert (zenon_L85_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H2e zenon_H1ac zenon_H2c zenon_H1ad. % 19.63/19.89 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((op2 (e20) (e20)) = (op2 (e21) (e20)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1ad. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1ae. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1b0]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e21) (e20)) = (op2 (e20) (e20)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1b0. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H2e. % 19.63/19.89 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.63/19.89 cut (((e21) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e21) = (op2 (e21) (e20)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1b1. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1ae. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H1b2]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H1b2 zenon_H1ac). % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 apply (zenon_L5_); trivial. % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L85_ *) % 19.63/19.89 assert (zenon_L86_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((op2 (e20) (e20)) = (op2 (e21) (e20)))) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> ((op2 (e23) (e23)) = (e23)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op2 (e21) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e22))\/((op2 (e21) (e21)) = (e23))))) -> (((op2 (e20) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e22) (e23)) = (e21))\/((op2 (e23) (e23)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1b3 zenon_H1ad zenon_H1a3 zenon_H192 zenon_H2c zenon_H74 zenon_Hb3 zenon_H67 zenon_H2e zenon_H1a1 zenon_Hdb zenon_H19b zenon_H198 zenon_H3e zenon_H1a0. % 19.63/19.89 apply (zenon_or_s _ _ zenon_H1b3); [ zenon_intro zenon_H1a2 | zenon_intro zenon_H1ac ]. % 19.63/19.89 apply (zenon_L84_); trivial. % 19.63/19.89 apply (zenon_L85_); trivial. % 19.63/19.89 (* end of lemma zenon_L86_ *) % 19.63/19.89 assert (zenon_L87_ : ((e20) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e23) (e23)) = (op2 (e21) (e20)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H2c zenon_H1b4 zenon_H1b5. % 19.63/19.89 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((op2 (e23) (e23)) = (op2 (e21) (e20)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1b5. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1ae. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e20) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1b6. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H2c. % 19.63/19.89 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 19.63/19.89 cut (((e20) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1b7]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H1ae | zenon_intro zenon_H1af ]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e20) = (op2 (e21) (e20)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1b7. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1ae. % 19.63/19.89 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1af]. % 19.63/19.89 cut (((op2 (e21) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1b8]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H1b8 zenon_H1b4). % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 apply zenon_H80. apply refl_equal. % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 apply zenon_H1af. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L87_ *) % 19.63/19.89 assert (zenon_L88_ : ((op2 (e21) (e22)) = (e20)) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1b9 zenon_H2c zenon_H1b4 zenon_H1ba. % 19.63/19.89 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1bc ]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((op2 (e21) (e20)) = (op2 (e21) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1ba. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1bb. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1bd]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e20) = (op2 (e23) (e23))) = ((op2 (e21) (e22)) = (op2 (e21) (e20)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1bd. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H2c. % 19.63/19.89 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 19.63/19.89 cut (((e20) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1bc ]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e20) = (op2 (e21) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1be. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1bb. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1bf]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H1bf zenon_H1b9). % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 apply (zenon_L87_); trivial. % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L88_ *) % 19.63/19.89 assert (zenon_L89_ : (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1c0 zenon_Ha7 zenon_H1c1. % 19.63/19.89 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (e21) (e21)) = (op2 (e21) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1c0. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Ha7. % 19.63/19.89 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 19.63/19.89 cut (((op2 (e21) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_Hb6. apply refl_equal. % 19.63/19.89 apply zenon_H1c2. apply sym_equal. exact zenon_H1c1. % 19.63/19.89 (* end of lemma zenon_L89_ *) % 19.63/19.89 assert (zenon_L90_ : (~((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e22)))) -> ((op2 (e21) (e23)) = (e22)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e22)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1c3 zenon_H1c4 zenon_H2e zenon_He3. % 19.63/19.89 cut (((op2 (e21) (e23)) = (e22)) = ((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1c3. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1c4. % 19.63/19.89 cut (((e22) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_He6]. % 19.63/19.89 cut (((op2 (e21) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H1c7 ]. % 19.63/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((op2 (e21) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1c5. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1c6. % 19.63/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 19.63/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 19.63/19.89 congruence. % 19.63/19.89 apply (zenon_L22_); trivial. % 19.63/19.89 apply zenon_H1c7. apply refl_equal. % 19.63/19.89 apply zenon_H1c7. apply refl_equal. % 19.63/19.89 apply zenon_He6. apply sym_equal. exact zenon_He3. % 19.63/19.89 (* end of lemma zenon_L90_ *) % 19.63/19.89 assert (zenon_L91_ : ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op2 (e21) (e22)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e20) (e22)) = (e22)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H67 zenon_H1c8 zenon_H1c4 zenon_He3 zenon_H2e zenon_H1c9. % 19.63/19.89 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1bc ]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((op2 (e20) (e22)) = (op2 (e21) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1c9. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1bb. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1ca]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((op2 (e21) (e22)) = (op2 (e20) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1ca. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H67. % 19.63/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1c3]. % 19.63/19.89 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1cb]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H1bb | zenon_intro zenon_H1bc ]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e22) = (op2 (e21) (e22)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1cb. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1bb. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1cc]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H1cc zenon_H1c8). % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 apply (zenon_L90_); trivial. % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 apply zenon_H1bc. apply refl_equal. % 19.63/19.89 (* end of lemma zenon_L91_ *) % 19.63/19.89 assert (zenon_L92_ : (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1cd zenon_Hfc zenon_H1ce. % 19.63/19.89 cut (((op1 (e11) (e11)) = (e11)) = ((op1 (e11) (e11)) = (op1 (e11) (e12)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1cd. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_Hfc. % 19.63/19.89 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1cf]. % 19.63/19.89 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 19.63/19.89 congruence. % 19.63/19.89 apply zenon_H176. apply refl_equal. % 19.63/19.89 apply zenon_H1cf. apply sym_equal. exact zenon_H1ce. % 19.63/19.89 (* end of lemma zenon_L92_ *) % 19.63/19.89 assert (zenon_L93_ : (~((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e12)))) -> ((op1 (e11) (e13)) = (e12)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e12)) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1d0 zenon_H107 zenon_H15 zenon_H146. % 19.63/19.89 cut (((op1 (e11) (e13)) = (e12)) = ((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e12)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1d0. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H107. % 19.63/19.89 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 19.63/19.89 cut (((op1 (e11) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))); [ zenon_intro zenon_H10b | zenon_intro zenon_H10c ]. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) = ((op1 (e11) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H10a. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H10b. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 19.63/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H6b]. % 19.63/19.89 congruence. % 19.63/19.89 apply (zenon_L19_); trivial. % 19.63/19.89 apply zenon_H10c. apply refl_equal. % 19.63/19.89 apply zenon_H10c. apply refl_equal. % 19.63/19.89 apply zenon_H14b. apply sym_equal. exact zenon_H146. % 19.63/19.89 (* end of lemma zenon_L93_ *) % 19.63/19.89 assert (zenon_L94_ : (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op1 (e11) (e12)) = (e13)) -> ((op2 (e21) (e22)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> False). % 19.63/19.89 do 0 intro. intros zenon_H1d1 zenon_H8b zenon_H1d2 zenon_H1d3 zenon_H52 zenon_H2e zenon_H66 zenon_H67. % 19.63/19.89 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1d1. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H8b. % 19.63/19.89 cut (((e23) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1d4]. % 19.63/19.89 cut (((h4 (e13)) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1d5]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [ zenon_intro zenon_H1d6 | zenon_intro zenon_H1d7 ]. % 19.63/19.89 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12)))) = ((h4 (e13)) = (h4 (op1 (e11) (e12))))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1d5. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1d6. % 19.63/19.89 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1d7]. % 19.63/19.89 cut (((h4 (op1 (e11) (e12))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1d8]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((op1 (e11) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H1d9]. % 19.63/19.89 congruence. % 19.63/19.89 exact (zenon_H1d9 zenon_H1d2). % 19.63/19.89 apply zenon_H1d7. apply refl_equal. % 19.63/19.89 apply zenon_H1d7. apply refl_equal. % 19.63/19.89 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H1da | zenon_intro zenon_H1db ]. % 19.63/19.89 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((e23) = (op2 (h4 (e11)) (h4 (e12))))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1d4. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1da. % 19.63/19.89 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 19.63/19.89 cut (((op2 (h4 (e11)) (h4 (e12))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1dc]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((op2 (e21) (e22)) = (e23)) = ((op2 (h4 (e11)) (h4 (e12))) = (e23))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1dc. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1d3. % 19.63/19.89 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 19.63/19.89 cut (((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1dd]. % 19.63/19.89 congruence. % 19.63/19.89 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H1da | zenon_intro zenon_H1db ]. % 19.63/19.89 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))). % 19.63/19.89 intro zenon_D_pnotp. % 19.63/19.89 apply zenon_H1dd. % 19.63/19.89 rewrite <- zenon_D_pnotp. % 19.63/19.89 exact zenon_H1da. % 19.63/19.89 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 19.63/19.89 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1de]. % 19.63/19.89 congruence. % 19.63/19.89 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.63/19.89 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 19.63/19.89 congruence. % 19.71/19.89 apply (zenon_L12_); trivial. % 19.71/19.89 apply (zenon_L17_); trivial. % 19.71/19.89 apply zenon_H1db. apply refl_equal. % 19.71/19.89 apply zenon_H1db. apply refl_equal. % 19.71/19.89 apply zenon_H72. apply refl_equal. % 19.71/19.89 apply zenon_H1db. apply refl_equal. % 19.71/19.89 apply zenon_H1db. apply refl_equal. % 19.71/19.89 (* end of lemma zenon_L94_ *) % 19.71/19.89 assert (zenon_L95_ : (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e10)) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e12)) -> ((op1 (e11) (e13)) = (e12)) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e21) (e22)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H1df zenon_H1e0 zenon_H12c zenon_H13 zenon_Hfc zenon_H1cd zenon_H1e1 zenon_H15 zenon_H146 zenon_H107 zenon_H6e zenon_H1d1 zenon_H8b zenon_H1d3 zenon_H52 zenon_H2e zenon_H66 zenon_H67. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H1df); [ zenon_intro zenon_H1e3 | zenon_intro zenon_H1e2 ]. % 19.71/19.89 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1e5 ]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1e0. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1e4. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((e10) = (op1 (e13) (e13))) = ((op1 (e11) (e12)) = (op1 (e11) (e10)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1e6. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H13. % 19.71/19.89 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12d]. % 19.71/19.89 cut (((e10) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1e7]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1e5 ]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e10) = (op1 (e11) (e12)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1e7. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1e4. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1e8]. % 19.71/19.89 congruence. % 19.71/19.89 exact (zenon_H1e8 zenon_H1e3). % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply (zenon_L58_); trivial. % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H1e2); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1e9 ]. % 19.71/19.89 apply (zenon_L92_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H1e9); [ zenon_intro zenon_H1ea | zenon_intro zenon_H1d2 ]. % 19.71/19.89 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1e5 ]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e10) (e12)) = (op1 (e11) (e12)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1e1. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1e4. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1eb]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) = ((op1 (e11) (e12)) = (op1 (e10) (e12)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1eb. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H6e. % 19.71/19.89 cut (((op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1d0]. % 19.71/19.89 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1ec]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H1e5 ]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e12) = (op1 (e11) (e12)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1ec. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1e4. % 19.71/19.89 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 19.71/19.89 cut (((op1 (e11) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 19.71/19.89 congruence. % 19.71/19.89 exact (zenon_H1ed zenon_H1ea). % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply (zenon_L93_); trivial. % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply zenon_H1e5. apply refl_equal. % 19.71/19.89 apply (zenon_L94_); trivial. % 19.71/19.89 (* end of lemma zenon_L95_ *) % 19.71/19.89 assert (zenon_L96_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e13)) = (e12))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e10) (e10)) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H157 zenon_H154 zenon_H15 zenon_H6e zenon_H6d zenon_H122 zenon_H67 zenon_H66 zenon_H2e zenon_H52 zenon_H1d3 zenon_H8b zenon_H1d1 zenon_H1e1 zenon_H1cd zenon_Hfc zenon_H1e0 zenon_H1df zenon_H11c zenon_H123 zenon_H5e zenon_H14d zenon_H14c zenon_Hf2 zenon_H60 zenon_H13e zenon_H13. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hef | zenon_intro zenon_H159 ]. % 19.71/19.89 exact (zenon_H154 zenon_Hef). % 19.71/19.89 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H12c | zenon_intro zenon_H15a ]. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H14f | zenon_intro zenon_H14e ]. % 19.71/19.89 exact (zenon_H14d zenon_H14f). % 19.71/19.89 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H5f | zenon_intro zenon_H150 ]. % 19.71/19.89 apply (zenon_L16_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H146 | zenon_intro zenon_H6f ]. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H6f | zenon_intro zenon_H124 ]. % 19.71/19.89 apply (zenon_L20_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H107 | zenon_intro zenon_H125 ]. % 19.71/19.89 apply (zenon_L95_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H11b | zenon_intro zenon_H126 ]. % 19.71/19.89 apply (zenon_L55_); trivial. % 19.71/19.89 exact (zenon_H123 zenon_H126). % 19.71/19.89 apply (zenon_L20_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H13f ]. % 19.71/19.89 apply (zenon_L47_); trivial. % 19.71/19.89 apply (zenon_L62_); trivial. % 19.71/19.89 (* end of lemma zenon_L96_ *) % 19.71/19.89 assert (zenon_L97_ : (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e20)) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e21) (e22)))) -> ((op2 (e20) (e22)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((op1 (e10) (e12)) = (op1 (e11) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e11))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e12)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e13)) = (e12))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e10) (e10)) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H1ee zenon_H1ba zenon_H1b4 zenon_H2c zenon_Ha7 zenon_H1c0 zenon_H1c9 zenon_He3 zenon_H1c4 zenon_H157 zenon_H154 zenon_H15 zenon_H6e zenon_H6d zenon_H122 zenon_H67 zenon_H66 zenon_H2e zenon_H52 zenon_H8b zenon_H1d1 zenon_H1e1 zenon_H1cd zenon_Hfc zenon_H1e0 zenon_H1df zenon_H11c zenon_H123 zenon_H5e zenon_H14d zenon_H14c zenon_Hf2 zenon_H60 zenon_H13e zenon_H13. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H1ee); [ zenon_intro zenon_H1b9 | zenon_intro zenon_H1ef ]. % 19.71/19.89 apply (zenon_L88_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H1ef); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H1f0 ]. % 19.71/19.89 apply (zenon_L89_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H1f0); [ zenon_intro zenon_H1c8 | zenon_intro zenon_H1d3 ]. % 19.71/19.89 apply (zenon_L91_); trivial. % 19.71/19.89 apply (zenon_L96_); trivial. % 19.71/19.89 (* end of lemma zenon_L97_ *) % 19.71/19.89 assert (zenon_L98_ : (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 19.71/19.89 do 0 intro. intros zenon_H1f1 zenon_Hce zenon_H1f2. % 19.71/19.89 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1f1. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_Hce. % 19.71/19.89 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1f3]. % 19.71/19.89 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_Ha2]. % 19.71/19.89 congruence. % 19.71/19.89 apply zenon_Ha2. apply refl_equal. % 19.71/19.89 apply zenon_H1f3. apply sym_equal. exact zenon_H1f2. % 19.71/19.89 (* end of lemma zenon_L98_ *) % 19.71/19.89 assert (zenon_L99_ : (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op1 (e11) (e13)) = (e12)) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H1f4 zenon_H66 zenon_H107 zenon_H8b zenon_H52. % 19.71/19.89 cut (((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1f4. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H66. % 19.71/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 19.71/19.89 cut (((h4 (e12)) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [ zenon_intro zenon_H1f7 | zenon_intro zenon_H1f8 ]. % 19.71/19.89 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13)))) = ((h4 (e12)) = (h4 (op1 (e11) (e13))))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1f6. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1f7. % 19.71/19.89 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 19.71/19.89 cut (((h4 (op1 (e11) (e13))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1fa]. % 19.71/19.89 congruence. % 19.71/19.89 exact (zenon_H1fa zenon_H107). % 19.71/19.89 apply zenon_H1f8. apply refl_equal. % 19.71/19.89 apply zenon_H1f8. apply refl_equal. % 19.71/19.89 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 19.71/19.89 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 19.71/19.89 congruence. % 19.71/19.89 apply zenon_H1fc. apply sym_equal. exact zenon_H52. % 19.71/19.89 apply zenon_H1fb. apply sym_equal. exact zenon_H8b. % 19.71/19.89 (* end of lemma zenon_L99_ *) % 19.71/19.89 assert (zenon_L100_ : (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e20)) = (e22)) -> ((op2 (e22) (e21)) = (e22)) -> False). % 19.71/19.89 do 0 intro. intros zenon_H1fd zenon_H15e zenon_H1fe. % 19.71/19.89 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (e22) (e20)) = (op2 (e22) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1fd. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H15e. % 19.71/19.89 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 19.71/19.89 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 19.71/19.89 congruence. % 19.71/19.89 apply zenon_H200. apply refl_equal. % 19.71/19.89 apply zenon_H1ff. apply sym_equal. exact zenon_H1fe. % 19.71/19.89 (* end of lemma zenon_L100_ *) % 19.71/19.89 assert (zenon_L101_ : (~((op2 (e23) (e23)) = (op2 (e20) (e21)))) -> ((op2 (e21) (e20)) = (e20)) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e20) (e21)) = (e20)) -> False). % 19.71/19.89 do 0 intro. intros zenon_H201 zenon_H1b4 zenon_H2c zenon_H56. % 19.71/19.89 cut (((op2 (e21) (e20)) = (e20)) = ((op2 (e23) (e23)) = (op2 (e20) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H201. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1b4. % 19.71/19.89 cut (((e20) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 19.71/19.89 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1b6]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H202 | zenon_intro zenon_H80 ]. % 19.71/19.89 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1b6. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H202. % 19.71/19.89 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 19.71/19.89 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 19.71/19.89 congruence. % 19.71/19.89 apply (zenon_L87_); trivial. % 19.71/19.89 apply zenon_H80. apply refl_equal. % 19.71/19.89 apply zenon_H80. apply refl_equal. % 19.71/19.89 apply zenon_H9d. apply sym_equal. exact zenon_H56. % 19.71/19.89 (* end of lemma zenon_L101_ *) % 19.71/19.89 assert (zenon_L102_ : ((op2 (e22) (e21)) = (e20)) -> ((op2 (e20) (e21)) = (e20)) -> ((op2 (e21) (e20)) = (e20)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H203 zenon_H56 zenon_H1b4 zenon_H2c zenon_H204. % 19.71/19.89 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H204. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H205. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((e20) = (op2 (e23) (e23))) = ((op2 (e22) (e21)) = (op2 (e20) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H207. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H2c. % 19.71/19.89 cut (((op2 (e23) (e23)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H201]. % 19.71/19.89 cut (((e20) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e20) = (op2 (e22) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H208. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H205. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H209]. % 19.71/19.89 congruence. % 19.71/19.89 exact (zenon_H209 zenon_H203). % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply (zenon_L101_); trivial. % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 (* end of lemma zenon_L102_ *) % 19.71/19.89 assert (zenon_L103_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e21) (e21)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H2e zenon_H20a zenon_H47 zenon_Ha7 zenon_H2c zenon_H20b. % 19.71/19.89 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H20b. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H205. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H20c]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e22) (e21)) = (op2 (e21) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H20c. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H2e. % 19.71/19.89 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 19.71/19.89 cut (((e21) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H20d]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e21) = (op2 (e22) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H20d. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H205. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H20e]. % 19.71/19.89 congruence. % 19.71/19.89 exact (zenon_H20e zenon_H20a). % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply (zenon_L32_); trivial. % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 (* end of lemma zenon_L103_ *) % 19.71/19.89 assert (zenon_L104_ : (~((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e23) (e21)))) -> ((op2 (e21) (e23)) = (e22)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e22)) -> False). % 19.71/19.89 do 0 intro. intros zenon_H20f zenon_H1c4 zenon_H2e zenon_H210. % 19.71/19.89 cut (((op2 (e21) (e23)) = (e22)) = ((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e23) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H20f. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1c4. % 19.71/19.89 cut (((e22) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H211]. % 19.71/19.89 cut (((op2 (e21) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c5]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [ zenon_intro zenon_H1c6 | zenon_intro zenon_H1c7 ]. % 19.71/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((op2 (e21) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1c5. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H1c6. % 19.71/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1c7]. % 19.71/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H73]. % 19.71/19.89 congruence. % 19.71/19.89 apply (zenon_L22_); trivial. % 19.71/19.89 apply zenon_H1c7. apply refl_equal. % 19.71/19.89 apply zenon_H1c7. apply refl_equal. % 19.71/19.89 apply zenon_H211. apply sym_equal. exact zenon_H210. % 19.71/19.89 (* end of lemma zenon_L104_ *) % 19.71/19.89 assert (zenon_L105_ : (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e23) (e21)) = (e22)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H212 zenon_H67 zenon_H1fe zenon_H1c4 zenon_H210 zenon_H2e. % 19.71/19.89 cut (((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((op2 (e22) (e21)) = (op2 (e23) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H212. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H67. % 19.71/19.89 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H20f]. % 19.71/19.89 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1ff]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H205 | zenon_intro zenon_H206 ]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e22) = (op2 (e22) (e21)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H1ff. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H205. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H206]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H213]. % 19.71/19.89 congruence. % 19.71/19.89 exact (zenon_H213 zenon_H1fe). % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply zenon_H206. apply refl_equal. % 19.71/19.89 apply (zenon_L104_); trivial. % 19.71/19.89 (* end of lemma zenon_L105_ *) % 19.71/19.89 assert (zenon_L106_ : (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((op1 (e12) (e11)) = (e13)) -> ((op2 (e22) (e21)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H214 zenon_H8b zenon_H215 zenon_H216 zenon_H66 zenon_H67 zenon_H52 zenon_H2e. % 19.71/19.89 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H214. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H8b. % 19.71/19.89 cut (((e23) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H217]. % 19.71/19.89 cut (((h4 (e13)) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H219 | zenon_intro zenon_H21a ]. % 19.71/19.89 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((h4 (e13)) = (h4 (op1 (e12) (e11))))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H218. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H219. % 19.71/19.89 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H21a]. % 19.71/19.89 cut (((h4 (op1 (e12) (e11))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H21b]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((op1 (e12) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H21c]. % 19.71/19.89 congruence. % 19.71/19.89 exact (zenon_H21c zenon_H215). % 19.71/19.89 apply zenon_H21a. apply refl_equal. % 19.71/19.89 apply zenon_H21a. apply refl_equal. % 19.71/19.89 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 19.71/19.89 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((e23) = (op2 (h4 (e12)) (h4 (e11))))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H217. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H21d. % 19.71/19.89 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 19.71/19.89 cut (((op2 (h4 (e12)) (h4 (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H21f]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((op2 (e22) (e21)) = (e23)) = ((op2 (h4 (e12)) (h4 (e11))) = (e23))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H21f. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H216. % 19.71/19.89 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 19.71/19.89 cut (((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H220]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H21d | zenon_intro zenon_H21e ]. % 19.71/19.89 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H220. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H21d. % 19.71/19.89 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 19.71/19.89 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 19.71/19.89 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.71/19.89 congruence. % 19.71/19.89 apply (zenon_L17_); trivial. % 19.71/19.89 apply (zenon_L12_); trivial. % 19.71/19.89 apply zenon_H21e. apply refl_equal. % 19.71/19.89 apply zenon_H21e. apply refl_equal. % 19.71/19.89 apply zenon_H72. apply refl_equal. % 19.71/19.89 apply zenon_H21e. apply refl_equal. % 19.71/19.89 apply zenon_H21e. apply refl_equal. % 19.71/19.89 (* end of lemma zenon_L106_ *) % 19.71/19.89 assert (zenon_L107_ : (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e10)) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (e13) (e13))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e10) (e10)) = (e11)) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e12)) -> ((op1 (e11) (e13)) = (e12)) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e22) (e21)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 19.71/19.89 do 0 intro. intros zenon_H222 zenon_H136 zenon_H12c zenon_H5e zenon_H223 zenon_H13 zenon_Hfc zenon_H4c zenon_H15 zenon_H108 zenon_H107 zenon_H6e zenon_H10d zenon_H214 zenon_H8b zenon_H216 zenon_H66 zenon_H67 zenon_H52 zenon_H2e. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H222); [ zenon_intro zenon_H135 | zenon_intro zenon_H224 ]. % 19.71/19.89 apply (zenon_L60_); trivial. % 19.71/19.89 apply (zenon_or_s _ _ zenon_H224); [ zenon_intro zenon_H226 | zenon_intro zenon_H225 ]. % 19.71/19.89 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 19.71/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H223. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H110. % 19.71/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 19.71/19.89 cut (((op1 (e12) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 19.71/19.89 congruence. % 19.71/19.89 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e12) (e11)) = (op1 (e11) (e11)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H227. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H15. % 19.71/19.89 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 19.71/19.89 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H228]. % 19.71/19.89 congruence. % 19.71/19.89 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H110 | zenon_intro zenon_H111 ]. % 19.71/19.89 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e11) = (op1 (e12) (e11)))). % 19.71/19.89 intro zenon_D_pnotp. % 19.71/19.89 apply zenon_H228. % 19.71/19.89 rewrite <- zenon_D_pnotp. % 19.71/19.89 exact zenon_H110. % 19.71/19.90 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H111]. % 19.71/19.90 cut (((op1 (e12) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H229 zenon_H226). % 19.71/19.90 apply zenon_H111. apply refl_equal. % 19.71/19.90 apply zenon_H111. apply refl_equal. % 19.71/19.90 apply (zenon_L49_); trivial. % 19.71/19.90 apply zenon_H111. apply refl_equal. % 19.71/19.90 apply zenon_H111. apply refl_equal. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H225); [ zenon_intro zenon_H10e | zenon_intro zenon_H215 ]. % 19.71/19.90 apply (zenon_L52_); trivial. % 19.71/19.90 apply (zenon_L106_); trivial. % 19.71/19.90 (* end of lemma zenon_L107_ *) % 19.71/19.90 assert (zenon_L108_ : (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (e12))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op2 (e22) (e21)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e13) (e13)) = (e12))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H157 zenon_H154 zenon_H25 zenon_H15 zenon_H1e zenon_H17 zenon_H22a zenon_H18a zenon_H118 zenon_Hf5 zenon_H102 zenon_H113 zenon_H114 zenon_H122 zenon_H6d zenon_H2e zenon_H52 zenon_H67 zenon_H66 zenon_H216 zenon_H8b zenon_H214 zenon_H10d zenon_Hfc zenon_H223 zenon_H5e zenon_H136 zenon_H222 zenon_H11c zenon_H6e zenon_H123 zenon_H49 zenon_Hf2 zenon_H60 zenon_H13e zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hef | zenon_intro zenon_H159 ]. % 19.71/19.90 exact (zenon_H154 zenon_Hef). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H12c | zenon_intro zenon_H15a ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H22a); [ zenon_intro zenon_H5f | zenon_intro zenon_H22b ]. % 19.71/19.90 apply (zenon_L16_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H22b); [ zenon_intro zenon_H188 | zenon_intro zenon_H22c ]. % 19.71/19.90 exact (zenon_H18a zenon_H188). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H10e | zenon_intro zenon_H108 ]. % 19.71/19.90 apply (zenon_L56_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H6f | zenon_intro zenon_H124 ]. % 19.71/19.90 apply (zenon_L20_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H107 | zenon_intro zenon_H125 ]. % 19.71/19.90 apply (zenon_L107_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H11b | zenon_intro zenon_H126 ]. % 19.71/19.90 apply (zenon_L55_); trivial. % 19.71/19.90 exact (zenon_H123 zenon_H126). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H16 | zenon_intro zenon_H4d ]. % 19.71/19.90 apply (zenon_L2_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H1d | zenon_intro zenon_H24 ]. % 19.71/19.90 apply (zenon_L3_); trivial. % 19.71/19.90 apply (zenon_L4_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H13f ]. % 19.71/19.90 apply (zenon_L47_); trivial. % 19.71/19.90 apply (zenon_L62_); trivial. % 19.71/19.90 (* end of lemma zenon_L108_ *) % 19.71/19.90 assert (zenon_L109_ : (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e20)) = (e20)) -> ((op2 (e20) (e21)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e21) (e21)) = (e21)) -> ((op2 (e20) (e20)) = (e21)) -> ((op2 (e23) (e21)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> (~((op1 (e11) (e11)) = (e12))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e13) (e13)) = (e12))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((e10) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H22d zenon_H204 zenon_H1b4 zenon_H56 zenon_H20b zenon_H2c zenon_Ha7 zenon_H47 zenon_H210 zenon_H1c4 zenon_H212 zenon_H157 zenon_H154 zenon_H25 zenon_H15 zenon_H1e zenon_H17 zenon_H22a zenon_H18a zenon_H118 zenon_Hf5 zenon_H102 zenon_H113 zenon_H114 zenon_H122 zenon_H6d zenon_H2e zenon_H52 zenon_H67 zenon_H66 zenon_H8b zenon_H214 zenon_H10d zenon_Hfc zenon_H223 zenon_H5e zenon_H136 zenon_H222 zenon_H11c zenon_H6e zenon_H123 zenon_H49 zenon_Hf2 zenon_H60 zenon_H13e zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H22d); [ zenon_intro zenon_H203 | zenon_intro zenon_H22e ]. % 19.71/19.90 apply (zenon_L102_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H20a | zenon_intro zenon_H22f ]. % 19.71/19.90 apply (zenon_L103_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H1fe | zenon_intro zenon_H216 ]. % 19.71/19.90 apply (zenon_L105_); trivial. % 19.71/19.90 apply (zenon_L108_); trivial. % 19.71/19.90 (* end of lemma zenon_L109_ *) % 19.71/19.90 assert (zenon_L110_ : ((~((op1 (e13) (e13)) = (e10)))\/((op1 (e13) (e10)) = (e13))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e22) (e21)) = (e23))))) -> (~((op1 (e10) (e10)) = (e10))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((e10) = (e12))) -> ((op1 (e10) (e11)) = (e10)) -> (~((op1 (e11) (e11)) = (e12))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> (((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e12) (e11)) = (e13))))) -> (((op1 (e10) (e11)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/((op1 (e13) (e11)) = (e12))))) -> ((op1 (e12) (e10)) = (e12)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op2 (e22) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e23)) = (e22))) -> (((op2 (e20) (e23)) = (e22))\/(((op2 (e21) (e23)) = (e22))\/(((op2 (e22) (e23)) = (e22))\/((op2 (e23) (e23)) = (e22))))) -> ((op2 (e22) (e20)) = (e22)) -> (~((op2 (e22) (e20)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (e22))) -> ((op2 (e20) (e21)) = (e20)) -> (~((e20) = (e22))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e21)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e20))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((~((op1 (e13) (e13)) = (e12)))\/((op1 (e13) (e12)) = (e13))) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H158 zenon_H230 zenon_H161 zenon_H231 zenon_H74 zenon_H67 zenon_H2e zenon_H22d zenon_H154 zenon_H49 zenon_H25 zenon_H1e zenon_H17 zenon_H60 zenon_H5e zenon_H18a zenon_H122 zenon_H11c zenon_Hf5 zenon_H102 zenon_Hfc zenon_H10d zenon_H113 zenon_H118 zenon_H15 zenon_H6e zenon_H6d zenon_H136 zenon_H223 zenon_H214 zenon_H8b zenon_H52 zenon_H66 zenon_H222 zenon_H22a zenon_Hf2 zenon_H13e zenon_H157 zenon_H212 zenon_Ha7 zenon_H20b zenon_H2c zenon_H204 zenon_Hd2 zenon_H232 zenon_H233 zenon_H15e zenon_H1fd zenon_H1ab zenon_H56 zenon_H58 zenon_H30 zenon_H37 zenon_H3e zenon_H44 zenon_H234 zenon_H143 zenon_H153 zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H123 | zenon_intro zenon_H144 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H9c | zenon_intro zenon_H235 ]. % 19.71/19.90 exact (zenon_H234 zenon_H9c). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H236 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H57 | zenon_intro zenon_H237 ]. % 19.71/19.90 apply (zenon_L14_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H238 ]. % 19.71/19.90 exact (zenon_H1ab zenon_H1a9). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1fe | zenon_intro zenon_H210 ]. % 19.71/19.90 apply (zenon_L100_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H75 | zenon_intro zenon_H239 ]. % 19.71/19.90 apply (zenon_L23_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H23a ]. % 19.71/19.90 apply (zenon_L109_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H23b ]. % 19.71/19.90 apply (zenon_L40_); trivial. % 19.71/19.90 exact (zenon_H232 zenon_H23b). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H2f | zenon_intro zenon_H48 ]. % 19.71/19.90 apply (zenon_L6_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H36 | zenon_intro zenon_H3d ]. % 19.71/19.90 apply (zenon_L7_); trivial. % 19.71/19.90 apply (zenon_L8_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H15f | zenon_intro zenon_H162 ]. % 19.71/19.90 apply (zenon_L69_); trivial. % 19.71/19.90 apply (zenon_L70_); trivial. % 19.71/19.90 apply (zenon_L63_); trivial. % 19.71/19.90 (* end of lemma zenon_L110_ *) % 19.71/19.90 assert (zenon_L111_ : ((~((op1 (e13) (e13)) = (e10)))\/((op1 (e13) (e10)) = (e13))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (((op1 (e13) (e11)) = (e10))\/(((op1 (e13) (e11)) = (e11))\/(((op1 (e13) (e11)) = (e12))\/((op1 (e13) (e11)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e12) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e13)) = (e12))\/(((op1 (e11) (e13)) = (e12))\/(((op1 (e12) (e13)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((~((op1 (e13) (e13)) = (e12)))\/((op1 (e13) (e12)) = (e13))) -> ((e10) = (op1 (e13) (e13))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H158 zenon_H49 zenon_H25 zenon_H1e zenon_H17 zenon_H6d zenon_H6e zenon_H15 zenon_H118 zenon_H113 zenon_H10e zenon_H10d zenon_Hfc zenon_H102 zenon_Hf5 zenon_H11c zenon_H122 zenon_H143 zenon_H153 zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H123 | zenon_intro zenon_H144 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 19.71/19.90 apply (zenon_L56_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H16 | zenon_intro zenon_H4d ]. % 19.71/19.90 apply (zenon_L2_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H1d | zenon_intro zenon_H24 ]. % 19.71/19.90 apply (zenon_L3_); trivial. % 19.71/19.90 apply (zenon_L4_); trivial. % 19.71/19.90 apply (zenon_L63_); trivial. % 19.71/19.90 (* end of lemma zenon_L111_ *) % 19.71/19.90 assert (zenon_L112_ : (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e10)) = (op2 (e23) (e23))) -> ((op1 (e12) (e12)) = (e10)) -> ((op2 (e22) (e22)) = (e20)) -> ((e20) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H23c zenon_H4f zenon_H15d zenon_Hc9 zenon_H2c zenon_H66 zenon_H67. % 19.71/19.90 cut (((h4 (e10)) = (op2 (e23) (e23))) = ((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H23c. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H4f. % 19.71/19.90 cut (((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H23d]. % 19.71/19.90 cut (((h4 (e10)) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [ zenon_intro zenon_H23f | zenon_intro zenon_H240 ]. % 19.71/19.90 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12)))) = ((h4 (e10)) = (h4 (op1 (e12) (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H23e. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H23f. % 19.71/19.90 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H240]. % 19.71/19.90 cut (((h4 (op1 (e12) (e12))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H241]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e12) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H156]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H156 zenon_H15d). % 19.71/19.90 apply zenon_H240. apply refl_equal. % 19.71/19.90 apply zenon_H240. apply refl_equal. % 19.71/19.90 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H242 | zenon_intro zenon_H243 ]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H23d. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H242. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H244]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e22) (e22)) = (e20)) = ((op2 (h4 (e12)) (h4 (e12))) = (op2 (e23) (e23)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H244. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_Hc9. % 19.71/19.90 cut (((e20) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 19.71/19.90 cut (((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H246]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H242 | zenon_intro zenon_H243 ]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H246. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H242. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H243]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H247]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.71/19.90 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.71/19.90 congruence. % 19.71/19.90 apply (zenon_L17_); trivial. % 19.71/19.90 apply (zenon_L17_); trivial. % 19.71/19.90 apply zenon_H243. apply refl_equal. % 19.71/19.90 apply zenon_H243. apply refl_equal. % 19.71/19.90 exact (zenon_H245 zenon_H2c). % 19.71/19.90 apply zenon_H243. apply refl_equal. % 19.71/19.90 apply zenon_H243. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L112_ *) % 19.71/19.90 assert (zenon_L113_ : (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e20) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e20)) -> False). % 19.71/19.90 do 0 intro. intros zenon_H248 zenon_H2c zenon_H249. % 19.71/19.90 cut (((e20) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H248. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H2c. % 19.71/19.90 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 19.71/19.90 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24a]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_Hd3 | zenon_intro zenon_Hd4 ]. % 19.71/19.90 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e20) = (op2 (e22) (e23)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H24a. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_Hd3. % 19.71/19.90 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_Hd4]. % 19.71/19.90 cut (((op2 (e22) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H24b]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H24b zenon_H249). % 19.71/19.90 apply zenon_Hd4. apply refl_equal. % 19.71/19.90 apply zenon_Hd4. apply refl_equal. % 19.71/19.90 apply zenon_H80. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L113_ *) % 19.71/19.90 assert (zenon_L114_ : ((~((op1 (e12) (e12)) = (e13)))\/((op1 (e12) (e13)) = (e12))) -> ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (op1 (op1 (e13) (e13)) (op1 (e13) (e13))) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e10)) = (op2 (e23) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e12) (e12)) = (e12))) -> (((op1 (e12) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e12)) = (e13))))) -> ((op2 (e20) (e21)) = (e20)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e22) (e20)) = (e22)) -> (~((e20) = (e22))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e20))\/((op2 (e23) (e20)) = (e20))))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H24c zenon_H15 zenon_H6e zenon_H11c zenon_H234 zenon_H24d zenon_H248 zenon_H23c zenon_H4f zenon_H67 zenon_H66 zenon_H24e zenon_H127 zenon_H24f zenon_H56 zenon_H2c zenon_H204 zenon_H15e zenon_H58 zenon_H161 zenon_H230. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H24c); [ zenon_intro zenon_H250 | zenon_intro zenon_H11b ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H9c | zenon_intro zenon_H235 ]. % 19.71/19.90 exact (zenon_H234 zenon_H9c). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H236 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H24d); [ zenon_intro zenon_H15f | zenon_intro zenon_H251 ]. % 19.71/19.90 apply (zenon_L69_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H251); [ zenon_intro zenon_H203 | zenon_intro zenon_H252 ]. % 19.71/19.90 apply (zenon_L102_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H252); [ zenon_intro zenon_Hc9 | zenon_intro zenon_H249 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H24f); [ zenon_intro zenon_H15d | zenon_intro zenon_H253 ]. % 19.71/19.90 apply (zenon_L112_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H253); [ zenon_intro zenon_H255 | zenon_intro zenon_H254 ]. % 19.71/19.90 exact (zenon_H24e zenon_H255). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H254); [ zenon_intro zenon_H12b | zenon_intro zenon_H256 ]. % 19.71/19.90 exact (zenon_H127 zenon_H12b). % 19.71/19.90 exact (zenon_H250 zenon_H256). % 19.71/19.90 apply (zenon_L113_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H15f | zenon_intro zenon_H162 ]. % 19.71/19.90 apply (zenon_L69_); trivial. % 19.71/19.90 apply (zenon_L70_); trivial. % 19.71/19.90 apply (zenon_L55_); trivial. % 19.71/19.90 (* end of lemma zenon_L114_ *) % 19.71/19.90 assert (zenon_L115_ : ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e21)) -> ((e20) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H2e zenon_H257 zenon_H2c zenon_H258. % 19.71/19.90 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H259 | zenon_intro zenon_H200 ]. % 19.71/19.90 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((op2 (e20) (e20)) = (op2 (e22) (e20)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H258. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H259. % 19.71/19.90 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 19.71/19.90 cut (((op2 (e22) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e22) (e20)) = (op2 (e20) (e20)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H25a. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H2e. % 19.71/19.90 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 19.71/19.90 cut (((e21) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H25b]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H259 | zenon_intro zenon_H200 ]. % 19.71/19.90 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e21) = (op2 (e22) (e20)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H25b. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H259. % 19.71/19.90 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 19.71/19.90 cut (((op2 (e22) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H25c zenon_H257). % 19.71/19.90 apply zenon_H200. apply refl_equal. % 19.71/19.90 apply zenon_H200. apply refl_equal. % 19.71/19.90 apply (zenon_L5_); trivial. % 19.71/19.90 apply zenon_H200. apply refl_equal. % 19.71/19.90 apply zenon_H200. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L115_ *) % 19.71/19.90 assert (zenon_L116_ : (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e11) (e11)) = (e11)) -> ((op1 (e11) (e13)) = (e11)) -> False). % 19.71/19.90 do 0 intro. intros zenon_H180 zenon_Hfc zenon_H168. % 19.71/19.90 cut (((op1 (e11) (e11)) = (e11)) = ((op1 (e11) (e11)) = (op1 (e11) (e13)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H180. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_Hfc. % 19.71/19.90 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 19.71/19.90 cut (((op1 (e11) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H176]. % 19.71/19.90 congruence. % 19.71/19.90 apply zenon_H176. apply refl_equal. % 19.71/19.90 apply zenon_H16c. apply sym_equal. exact zenon_H168. % 19.71/19.90 (* end of lemma zenon_L116_ *) % 19.71/19.90 assert (zenon_L117_ : (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op1 (e12) (e13)) = (e11)) -> ((op2 (e22) (e23)) = (e21)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 19.71/19.90 do 0 intro. intros zenon_H25d zenon_H52 zenon_H16e zenon_Hb8 zenon_H2e zenon_H66 zenon_H67 zenon_H8b. % 19.71/19.90 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H25d. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H52. % 19.71/19.90 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 19.71/19.90 cut (((h4 (e11)) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H25f]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [ zenon_intro zenon_H260 | zenon_intro zenon_H261 ]. % 19.71/19.90 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13)))) = ((h4 (e11)) = (h4 (op1 (e12) (e13))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H25f. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H260. % 19.71/19.90 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H261]. % 19.71/19.90 cut (((h4 (op1 (e12) (e13))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H262]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H172]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H172 zenon_H16e). % 19.71/19.90 apply zenon_H261. apply refl_equal. % 19.71/19.90 apply zenon_H261. apply refl_equal. % 19.71/19.90 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H263 | zenon_intro zenon_H264 ]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H25e. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H263. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H265]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e22) (e23)) = (e21)) = ((op2 (h4 (e12)) (h4 (e13))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H265. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_Hb8. % 19.71/19.90 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 19.71/19.90 cut (((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H267]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H263 | zenon_intro zenon_H264 ]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H267. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H263. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H268]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 19.71/19.90 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.71/19.90 congruence. % 19.71/19.90 apply (zenon_L17_); trivial. % 19.71/19.90 exact (zenon_H97 zenon_H8b). % 19.71/19.90 apply zenon_H264. apply refl_equal. % 19.71/19.90 apply zenon_H264. apply refl_equal. % 19.71/19.90 exact (zenon_H266 zenon_H2e). % 19.71/19.90 apply zenon_H264. apply refl_equal. % 19.71/19.90 apply zenon_H264. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L117_ *) % 19.71/19.90 assert (zenon_L118_ : ((h4 (e13)) = (e23)) -> ((op1 (e13) (e10)) = (e13)) -> (~((e23) = (h4 (op1 (e13) (e10))))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H8b zenon_H114 zenon_H269. % 19.71/19.90 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H26a | zenon_intro zenon_H26b ]. % 19.71/19.90 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((e23) = (h4 (op1 (e13) (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H269. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H26a. % 19.71/19.90 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 19.71/19.90 cut (((h4 (op1 (e13) (e10))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H26c]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e13) (e10))) = (e23))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H26c. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H8b. % 19.71/19.90 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H72]. % 19.71/19.90 cut (((h4 (e13)) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H26d]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H26a | zenon_intro zenon_H26b ]. % 19.71/19.90 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((h4 (e13)) = (h4 (op1 (e13) (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H26d. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H26a. % 19.71/19.90 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 19.71/19.90 cut (((h4 (op1 (e13) (e10))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e13) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H26f zenon_H114). % 19.71/19.90 apply zenon_H26b. apply refl_equal. % 19.71/19.90 apply zenon_H26b. apply refl_equal. % 19.71/19.90 apply zenon_H72. apply refl_equal. % 19.71/19.90 apply zenon_H26b. apply refl_equal. % 19.71/19.90 apply zenon_H26b. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L118_ *) % 19.71/19.90 assert (zenon_L119_ : ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op1 (e13) (e11)) = (e12)) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> (~((e22) = (h4 (op1 (e13) (e11))))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H66 zenon_H108 zenon_H67 zenon_H270. % 19.71/19.90 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H271 | zenon_intro zenon_H272 ]. % 19.71/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((e22) = (h4 (op1 (e13) (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H270. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H271. % 19.71/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 19.71/19.90 cut (((h4 (op1 (e13) (e11))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H273]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e13) (e11))) = (e22))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H273. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H66. % 19.71/19.90 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H68]. % 19.71/19.90 cut (((h4 (e12)) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H274]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H271 | zenon_intro zenon_H272 ]. % 19.71/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((h4 (e12)) = (h4 (op1 (e13) (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H274. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H271. % 19.71/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 19.71/19.90 cut (((h4 (op1 (e13) (e11))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H275]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e13) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H276]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H276 zenon_H108). % 19.71/19.90 apply zenon_H272. apply refl_equal. % 19.71/19.90 apply zenon_H272. apply refl_equal. % 19.71/19.90 apply zenon_H68. apply sym_equal. exact zenon_H67. % 19.71/19.90 apply zenon_H272. apply refl_equal. % 19.71/19.90 apply zenon_H272. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L119_ *) % 19.71/19.90 assert (zenon_L120_ : ((op2 (e23) (e21)) = (e22)) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((op1 (e13) (e11)) = (e12)) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H210 zenon_H8b zenon_H52 zenon_H2e zenon_H66 zenon_H67 zenon_H108 zenon_H277. % 19.71/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H278 | zenon_intro zenon_H279 ]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H277. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H278. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H27a]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e23) (e21)) = (e22)) = ((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H27a. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H210. % 19.71/19.90 cut (((e22) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H270]. % 19.71/19.90 cut (((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H27b]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H278 | zenon_intro zenon_H279 ]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H27b. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H278. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H279]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H27c]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 19.71/19.90 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H97 zenon_H8b). % 19.71/19.90 apply (zenon_L12_); trivial. % 19.71/19.90 apply zenon_H279. apply refl_equal. % 19.71/19.90 apply zenon_H279. apply refl_equal. % 19.71/19.90 apply (zenon_L119_); trivial. % 19.71/19.90 apply zenon_H279. apply refl_equal. % 19.71/19.90 apply zenon_H279. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L120_ *) % 19.71/19.90 assert (zenon_L121_ : ((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e11)) -> ((e10) = (op1 (e13) (e13))) -> (~((op1 (e10) (e10)) = (op1 (e13) (e10)))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H15 zenon_H27d zenon_H13 zenon_H27e. % 19.71/19.90 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H141 | zenon_intro zenon_H117 ]. % 19.71/19.90 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((op1 (e10) (e10)) = (op1 (e13) (e10)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H27e. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H141. % 19.71/19.90 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 19.71/19.90 cut (((op1 (e13) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H27f]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((e11) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e13) (e10)) = (op1 (e10) (e10)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H27f. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H15. % 19.71/19.90 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 19.71/19.90 cut (((e11) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H280]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H141 | zenon_intro zenon_H117 ]. % 19.71/19.90 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e11) = (op1 (e13) (e10)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H280. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H141. % 19.71/19.90 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 19.71/19.90 cut (((op1 (e13) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H281]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H281 zenon_H27d). % 19.71/19.90 apply zenon_H117. apply refl_equal. % 19.71/19.90 apply zenon_H117. apply refl_equal. % 19.71/19.90 apply (zenon_L1_); trivial. % 19.71/19.90 apply zenon_H117. apply refl_equal. % 19.71/19.90 apply zenon_H117. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L121_ *) % 19.71/19.90 assert (zenon_L122_ : ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op1 (e13) (e12)) = (e11)) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((e21) = (h4 (op1 (e13) (e12))))) -> False). % 19.71/19.90 do 0 intro. intros zenon_H52 zenon_H282 zenon_H2e zenon_H283. % 19.71/19.90 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H284 | zenon_intro zenon_H285 ]. % 19.71/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((e21) = (h4 (op1 (e13) (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H283. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H284. % 19.71/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H285]. % 19.71/19.90 cut (((h4 (op1 (e13) (e12))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e13) (e12))) = (e21))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H286. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H52. % 19.71/19.90 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 19.71/19.90 cut (((h4 (e11)) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H284 | zenon_intro zenon_H285 ]. % 19.71/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((h4 (e11)) = (h4 (op1 (e13) (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H287. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H284. % 19.71/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H285]. % 19.71/19.90 cut (((h4 (op1 (e13) (e12))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H288]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e13) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H289 zenon_H282). % 19.71/19.90 apply zenon_H285. apply refl_equal. % 19.71/19.90 apply zenon_H285. apply refl_equal. % 19.71/19.90 apply zenon_H53. apply sym_equal. exact zenon_H2e. % 19.71/19.90 apply zenon_H285. apply refl_equal. % 19.71/19.90 apply zenon_H285. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L122_ *) % 19.71/19.90 assert (zenon_L123_ : ((op2 (e23) (e22)) = (e21)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) -> ((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op1 (e13) (e12)) = (e11)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> False). % 19.71/19.90 do 0 intro. intros zenon_Hbb zenon_H8b zenon_H66 zenon_H67 zenon_H52 zenon_H2e zenon_H282 zenon_H28a. % 19.71/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H28b | zenon_intro zenon_H28c ]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H28a. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H28b. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e23) (e22)) = (e21)) = ((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H28d. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_Hbb. % 19.71/19.90 cut (((e21) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 19.71/19.90 cut (((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H28b | zenon_intro zenon_H28c ]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H28e. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H28b. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H28c]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H28f]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.71/19.90 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H97 zenon_H8b). % 19.71/19.90 apply (zenon_L17_); trivial. % 19.71/19.90 apply zenon_H28c. apply refl_equal. % 19.71/19.90 apply zenon_H28c. apply refl_equal. % 19.71/19.90 apply (zenon_L122_); trivial. % 19.71/19.90 apply zenon_H28c. apply refl_equal. % 19.71/19.90 apply zenon_H28c. apply refl_equal. % 19.71/19.90 (* end of lemma zenon_L123_ *) % 19.71/19.90 assert (zenon_L124_ : (~((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (e23) (e23))) -> ((e10) = (op1 (e13) (e13))) -> ((h4 (e13)) = (e23)) -> False). % 19.71/19.90 do 0 intro. intros zenon_H290 zenon_H4f zenon_H13 zenon_H8b. % 19.71/19.90 cut (((h4 (e10)) = (op2 (e23) (e23))) = ((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H290. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H4f. % 19.71/19.90 cut (((op2 (e23) (e23)) = (op2 (h4 (e13)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 19.71/19.90 cut (((h4 (e10)) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [ zenon_intro zenon_H293 | zenon_intro zenon_H294 ]. % 19.71/19.90 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13)))) = ((h4 (e10)) = (h4 (op1 (e13) (e13))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H292. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H293. % 19.71/19.90 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 19.71/19.90 cut (((h4 (op1 (e13) (e13))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H295]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e13) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H14]. % 19.71/19.90 congruence. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply zenon_H294. apply refl_equal. % 19.71/19.90 apply zenon_H294. apply refl_equal. % 19.71/19.90 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 19.71/19.90 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H1fb]. % 19.71/19.90 congruence. % 19.71/19.90 apply zenon_H1fb. apply sym_equal. exact zenon_H8b. % 19.71/19.90 apply zenon_H1fb. apply sym_equal. exact zenon_H8b. % 19.71/19.90 (* end of lemma zenon_L124_ *) % 19.71/19.90 assert (zenon_L125_ : (~(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23)))))) -> ((h4 (e13)) = (e23)) -> False). % 19.71/19.90 do 0 intro. intros zenon_H296 zenon_H8b. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H296). zenon_intro zenon_H298. zenon_intro zenon_H297. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H297). zenon_intro zenon_H29a. zenon_intro zenon_H299. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H299). zenon_intro zenon_H29b. zenon_intro zenon_H97. % 19.71/19.90 exact (zenon_H97 zenon_H8b). % 19.71/19.90 (* end of lemma zenon_L125_ *) % 19.71/19.90 apply NNPP. intro zenon_G. % 19.71/19.90 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H29d. zenon_intro zenon_H29c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H29c). zenon_intro zenon_H29f. zenon_intro zenon_H29e. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H29e). zenon_intro zenon_H2a1. zenon_intro zenon_H2a0. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2a0). zenon_intro zenon_H98. zenon_intro zenon_H2a2. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2a2). zenon_intro zenon_H2a4. zenon_intro zenon_H2a3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2a3). zenon_intro zenon_H17f. zenon_intro zenon_H2a5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2a5). zenon_intro zenon_H1df. zenon_intro zenon_H2a6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2a6). zenon_intro zenon_H2a8. zenon_intro zenon_H2a7. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2a7). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H222. zenon_intro zenon_H2ab. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H24f. zenon_intro zenon_H2ac. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ac). zenon_intro zenon_H2ae. zenon_intro zenon_H2ad. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ad). zenon_intro zenon_H2b0. zenon_intro zenon_H2af. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H118. zenon_intro zenon_H2b1. % 19.71/19.90 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H2b3. zenon_intro zenon_H2b2. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2b2). zenon_intro zenon_H157. zenon_intro zenon_H2b4. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2b4). zenon_intro zenon_H49. zenon_intro zenon_H2b5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2b5). zenon_intro zenon_H2b7. zenon_intro zenon_H2b6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2b6). zenon_intro zenon_H14c. zenon_intro zenon_H2b8. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2b8). zenon_intro zenon_H2ba. zenon_intro zenon_H2b9. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2b9). zenon_intro zenon_H2bc. zenon_intro zenon_H2bb. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2bb). zenon_intro zenon_H2be. zenon_intro zenon_H2bd. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2bd). zenon_intro zenon_H2c0. zenon_intro zenon_H2bf. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2bf). zenon_intro zenon_H2c2. zenon_intro zenon_H2c1. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2c1). zenon_intro zenon_H2c4. zenon_intro zenon_H2c3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2c3). zenon_intro zenon_H2c6. zenon_intro zenon_H2c5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2c5). zenon_intro zenon_H2c8. zenon_intro zenon_H2c7. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2c7). zenon_intro zenon_H22a. zenon_intro zenon_H2c9. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2c9). zenon_intro zenon_H2cb. zenon_intro zenon_H2ca. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ca). zenon_intro zenon_H2cd. zenon_intro zenon_H2cc. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2cc). zenon_intro zenon_H155. zenon_intro zenon_H2ce. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ce). zenon_intro zenon_H2d0. zenon_intro zenon_H2cf. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2cf). zenon_intro zenon_H2d2. zenon_intro zenon_H2d1. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2d1). zenon_intro zenon_H2d4. zenon_intro zenon_H2d3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2d3). zenon_intro zenon_H128. zenon_intro zenon_H2d5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2d5). zenon_intro zenon_H2d7. zenon_intro zenon_H2d6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2d6). zenon_intro zenon_H2d9. zenon_intro zenon_H2d8. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2d8). zenon_intro zenon_H2db. zenon_intro zenon_H2da. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2da). zenon_intro zenon_H2dd. zenon_intro zenon_H2dc. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2dc). zenon_intro zenon_H2df. zenon_intro zenon_H2de. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2de). zenon_intro zenon_H2e1. zenon_intro zenon_H2e0. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2e0). zenon_intro zenon_H17b. zenon_intro zenon_H2e2. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2e2). zenon_intro zenon_H2e4. zenon_intro zenon_H2e3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2e3). zenon_intro zenon_H122. zenon_intro zenon_H2e5. % 19.71/19.90 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H2e7. zenon_intro zenon_H2e6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2e6). zenon_intro zenon_H2e9. zenon_intro zenon_H2e8. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2e8). zenon_intro zenon_H2eb. zenon_intro zenon_H2ea. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ea). zenon_intro zenon_H2ed. zenon_intro zenon_H2ec. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ec). zenon_intro zenon_H2ef. zenon_intro zenon_H2ee. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ee). zenon_intro zenon_H1a1. zenon_intro zenon_H2f0. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2f0). zenon_intro zenon_H1ee. zenon_intro zenon_H2f1. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2f1). zenon_intro zenon_H2f3. zenon_intro zenon_H2f2. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2f2). zenon_intro zenon_H2f5. zenon_intro zenon_H2f4. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2f4). zenon_intro zenon_H22d. zenon_intro zenon_H2f6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2f6). zenon_intro zenon_Hc4. zenon_intro zenon_H2f7. % 19.71/19.90 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H2f9. zenon_intro zenon_H2f8. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2f8). zenon_intro zenon_H230. zenon_intro zenon_H2fa. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2fa). zenon_intro zenon_H44. zenon_intro zenon_H2fb. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2fb). zenon_intro zenon_H2fd. zenon_intro zenon_H2fc. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2fc). zenon_intro zenon_He7. zenon_intro zenon_H2fe. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2fe). zenon_intro zenon_H300. zenon_intro zenon_H2ff. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H2ff). zenon_intro zenon_H302. zenon_intro zenon_H301. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H301). zenon_intro zenon_H304. zenon_intro zenon_H303. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H303). zenon_intro zenon_H306. zenon_intro zenon_H305. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H305). zenon_intro zenon_H308. zenon_intro zenon_H307. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H307). zenon_intro zenon_H30a. zenon_intro zenon_H309. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H309). zenon_intro zenon_H30c. zenon_intro zenon_H30b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H30b). zenon_intro zenon_H30e. zenon_intro zenon_H30d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H30d). zenon_intro zenon_H231. zenon_intro zenon_H30f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H30f). zenon_intro zenon_H311. zenon_intro zenon_H310. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H310). zenon_intro zenon_H313. zenon_intro zenon_H312. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H312). zenon_intro zenon_H24d. zenon_intro zenon_H314. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H314). zenon_intro zenon_H316. zenon_intro zenon_H315. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H315). zenon_intro zenon_H318. zenon_intro zenon_H317. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H317). zenon_intro zenon_H31a. zenon_intro zenon_H319. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H319). zenon_intro zenon_H31c. zenon_intro zenon_H31b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H31b). zenon_intro zenon_H31e. zenon_intro zenon_H31d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H31d). zenon_intro zenon_H320. zenon_intro zenon_H31f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H31f). zenon_intro zenon_H322. zenon_intro zenon_H321. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H321). zenon_intro zenon_H324. zenon_intro zenon_H323. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H323). zenon_intro zenon_H326. zenon_intro zenon_H325. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H325). zenon_intro zenon_Hda. zenon_intro zenon_H327. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H327). zenon_intro zenon_Hdb. zenon_intro zenon_H328. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H328). zenon_intro zenon_H32a. zenon_intro zenon_H329. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H329). zenon_intro zenon_H233. zenon_intro zenon_H32b. % 19.71/19.90 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H18c. zenon_intro zenon_H32c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H32c). zenon_intro zenon_H32e. zenon_intro zenon_H32d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H32d). zenon_intro zenon_H27e. zenon_intro zenon_H32f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H32f). zenon_intro zenon_H331. zenon_intro zenon_H330. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H330). zenon_intro zenon_H333. zenon_intro zenon_H332. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H332). zenon_intro zenon_H335. zenon_intro zenon_H334. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H334). zenon_intro zenon_H174. zenon_intro zenon_H336. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H336). zenon_intro zenon_H136. zenon_intro zenon_H337. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H337). zenon_intro zenon_H339. zenon_intro zenon_H338. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H338). zenon_intro zenon_H223. zenon_intro zenon_H33a. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H33a). zenon_intro zenon_H102. zenon_intro zenon_H33b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H33b). zenon_intro zenon_H10d. zenon_intro zenon_H33c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H33c). zenon_intro zenon_H1e1. zenon_intro zenon_H33d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H33d). zenon_intro zenon_H147. zenon_intro zenon_H33e. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H33e). zenon_intro zenon_H340. zenon_intro zenon_H33f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H33f). zenon_intro zenon_H342. zenon_intro zenon_H341. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H341). zenon_intro zenon_H344. zenon_intro zenon_H343. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H343). zenon_intro zenon_H346. zenon_intro zenon_H345. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H345). zenon_intro zenon_H6d. zenon_intro zenon_H347. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H347). zenon_intro zenon_H16f. zenon_intro zenon_H348. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H348). zenon_intro zenon_H83. zenon_intro zenon_H349. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H349). zenon_intro zenon_H11c. zenon_intro zenon_H34a. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H34a). zenon_intro zenon_H34c. zenon_intro zenon_H34b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H34b). zenon_intro zenon_H13a. zenon_intro zenon_H34d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H34d). zenon_intro zenon_H17. zenon_intro zenon_H34e. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H34e). zenon_intro zenon_H1e. zenon_intro zenon_H34f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H34f). zenon_intro zenon_H25. zenon_intro zenon_H350. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H350). zenon_intro zenon_H78. zenon_intro zenon_H351. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H351). zenon_intro zenon_H353. zenon_intro zenon_H352. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H352). zenon_intro zenon_H355. zenon_intro zenon_H354. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H354). zenon_intro zenon_H357. zenon_intro zenon_H356. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H356). zenon_intro zenon_H1e0. zenon_intro zenon_H358. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H358). zenon_intro zenon_H35a. zenon_intro zenon_H359. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H359). zenon_intro zenon_H1cd. zenon_intro zenon_H35b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H35b). zenon_intro zenon_H180. zenon_intro zenon_H35c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H35c). zenon_intro zenon_H35e. zenon_intro zenon_H35d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H35d). zenon_intro zenon_H360. zenon_intro zenon_H35f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H35f). zenon_intro zenon_H362. zenon_intro zenon_H361. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H361). zenon_intro zenon_H364. zenon_intro zenon_H363. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H363). zenon_intro zenon_H366. zenon_intro zenon_H365. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H365). zenon_intro zenon_H368. zenon_intro zenon_H367. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H367). zenon_intro zenon_H36a. zenon_intro zenon_H369. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H369). zenon_intro zenon_H113. zenon_intro zenon_H36b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H36b). zenon_intro zenon_H143. zenon_intro zenon_H36c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H36c). zenon_intro zenon_H13e. zenon_intro zenon_H36d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H36d). zenon_intro zenon_H36f. zenon_intro zenon_H36e. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H36e). zenon_intro zenon_Hf5. zenon_intro zenon_H370. % 19.71/19.90 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H1ad. zenon_intro zenon_H371. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H371). zenon_intro zenon_H258. zenon_intro zenon_H372. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H372). zenon_intro zenon_Ha0. zenon_intro zenon_H373. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H373). zenon_intro zenon_H375. zenon_intro zenon_H374. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H374). zenon_intro zenon_H377. zenon_intro zenon_H376. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H376). zenon_intro zenon_H379. zenon_intro zenon_H378. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H378). zenon_intro zenon_H19b. zenon_intro zenon_H37a. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H37a). zenon_intro zenon_H204. zenon_intro zenon_H37b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H37b). zenon_intro zenon_H37d. zenon_intro zenon_H37c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H37c). zenon_intro zenon_H20b. zenon_intro zenon_H37e. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H37e). zenon_intro zenon_Had. zenon_intro zenon_H37f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H37f). zenon_intro zenon_H212. zenon_intro zenon_H380. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H380). zenon_intro zenon_H1c9. zenon_intro zenon_H381. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H381). zenon_intro zenon_He4. zenon_intro zenon_H382. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H382). zenon_intro zenon_H384. zenon_intro zenon_H383. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H383). zenon_intro zenon_H386. zenon_intro zenon_H385. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H385). zenon_intro zenon_H388. zenon_intro zenon_H387. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H387). zenon_intro zenon_Hbe. zenon_intro zenon_H389. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H389). zenon_intro zenon_H74. zenon_intro zenon_H38a. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H38a). zenon_intro zenon_H198. zenon_intro zenon_H38b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H38b). zenon_intro zenon_H7e. zenon_intro zenon_H38c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H38c). zenon_intro zenon_Hd2. zenon_intro zenon_H38d. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H38d). zenon_intro zenon_H38f. zenon_intro zenon_H38e. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H38e). zenon_intro zenon_H248. zenon_intro zenon_H390. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H390). zenon_intro zenon_H30. zenon_intro zenon_H391. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H391). zenon_intro zenon_H37. zenon_intro zenon_H392. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H392). zenon_intro zenon_H3e. zenon_intro zenon_H393. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H393). zenon_intro zenon_H7b. zenon_intro zenon_H394. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H394). zenon_intro zenon_H396. zenon_intro zenon_H395. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H395). zenon_intro zenon_H398. zenon_intro zenon_H397. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H397). zenon_intro zenon_H39a. zenon_intro zenon_H399. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H399). zenon_intro zenon_H1ba. zenon_intro zenon_H39b. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H39b). zenon_intro zenon_H39d. zenon_intro zenon_H39c. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H39c). zenon_intro zenon_H1c0. zenon_intro zenon_H39e. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H39e). zenon_intro zenon_Hb3. zenon_intro zenon_H39f. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H39f). zenon_intro zenon_H3a1. zenon_intro zenon_H3a0. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3a0). zenon_intro zenon_H1fd. zenon_intro zenon_H3a2. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3a2). zenon_intro zenon_H3a4. zenon_intro zenon_H3a3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3a3). zenon_intro zenon_H3a6. zenon_intro zenon_H3a5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3a5). zenon_intro zenon_H3a8. zenon_intro zenon_H3a7. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3a7). zenon_intro zenon_H3aa. zenon_intro zenon_H3a9. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3a9). zenon_intro zenon_H3ac. zenon_intro zenon_H3ab. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3ab). zenon_intro zenon_Hcd. zenon_intro zenon_H3ad. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3ad). zenon_intro zenon_H1f1. zenon_intro zenon_H3ae. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3ae). zenon_intro zenon_H161. zenon_intro zenon_H3af. % 19.71/19.90 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H3b1. zenon_intro zenon_H3b0. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3b0). zenon_intro zenon_H60. zenon_intro zenon_H3b2. % 19.71/19.90 apply (zenon_and_s _ _ ax8). zenon_intro zenon_H3b4. zenon_intro zenon_H3b3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3b3). zenon_intro zenon_H58. zenon_intro zenon_H3b5. % 19.71/19.90 apply (zenon_and_s _ _ ax10). zenon_intro zenon_H3b7. zenon_intro zenon_H3b6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3b6). zenon_intro zenon_H3b9. zenon_intro zenon_H3b8. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3b8). zenon_intro zenon_Hee. zenon_intro zenon_H3ba. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3ba). zenon_intro zenon_H151. zenon_intro zenon_H3bb. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3bb). zenon_intro zenon_H3bd. zenon_intro zenon_H3bc. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3bc). zenon_intro zenon_H190. zenon_intro zenon_H3be. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3be). zenon_intro zenon_H17e. zenon_intro zenon_H3bf. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3bf). zenon_intro zenon_H3c1. zenon_intro zenon_H3c0. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3c0). zenon_intro zenon_H182. zenon_intro zenon_H3c2. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3c2). zenon_intro zenon_H3c4. zenon_intro zenon_H3c3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3c3). zenon_intro zenon_H3c6. zenon_intro zenon_H3c5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3c5). zenon_intro zenon_H152. zenon_intro zenon_H3c7. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3c7). zenon_intro zenon_H24c. zenon_intro zenon_H3c8. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3c8). zenon_intro zenon_H158. zenon_intro zenon_H3c9. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3c9). zenon_intro zenon_H3cb. zenon_intro zenon_H3ca. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3ca). zenon_intro zenon_H153. zenon_intro zenon_H3cc. % 19.71/19.90 apply (zenon_and_s _ _ ax11). zenon_intro zenon_H3ce. zenon_intro zenon_H3cd. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3cd). zenon_intro zenon_H3d0. zenon_intro zenon_H3cf. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3cf). zenon_intro zenon_H9b. zenon_intro zenon_H3d1. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3d1). zenon_intro zenon_He8. zenon_intro zenon_H3d2. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3d2). zenon_intro zenon_H3d4. zenon_intro zenon_H3d3. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3d3). zenon_intro zenon_H1b3. zenon_intro zenon_H3d5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3d5). zenon_intro zenon_H1a0. zenon_intro zenon_H3d6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3d6). zenon_intro zenon_H3d8. zenon_intro zenon_H3d7. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3d7). zenon_intro zenon_H1a3. zenon_intro zenon_H3d9. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3d9). zenon_intro zenon_H3db. zenon_intro zenon_H3da. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3da). zenon_intro zenon_H3dd. zenon_intro zenon_H3dc. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3dc). zenon_intro zenon_Hed. zenon_intro zenon_H3de. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3de). zenon_intro zenon_Hd8. zenon_intro zenon_H3df. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3df). zenon_intro zenon_Hdc. zenon_intro zenon_H3e0. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3e0). zenon_intro zenon_Hd9. zenon_intro zenon_H3e1. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3e1). zenon_intro zenon_H3e3. zenon_intro zenon_H3e2. % 19.71/19.90 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H13. zenon_intro zenon_H3e4. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3e4). zenon_intro zenon_H15. zenon_intro zenon_H6e. % 19.71/19.90 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H2c. zenon_intro zenon_H3e5. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3e5). zenon_intro zenon_H2e. zenon_intro zenon_H67. % 19.71/19.90 apply (zenon_and_s _ _ ax17). zenon_intro zenon_H8b. zenon_intro zenon_H3e6. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3e6). zenon_intro zenon_H4f. zenon_intro zenon_H3e7. % 19.71/19.90 apply (zenon_and_s _ _ zenon_H3e7). zenon_intro zenon_H52. zenon_intro zenon_H66. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H3e9. zenon_intro zenon_H3e8. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H3e8). zenon_intro zenon_H3eb. zenon_intro zenon_H3ea. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H3ea). zenon_intro zenon_H3ed. zenon_intro zenon_H3ec. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H3ec); [ zenon_intro zenon_H3ef | zenon_intro zenon_H3ee ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 19.71/19.90 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H3ef. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H52. % 19.71/19.90 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3f0]. % 19.71/19.90 cut (((h4 (e11)) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3f1]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [ zenon_intro zenon_H3f2 | zenon_intro zenon_H3f3 ]. % 19.71/19.90 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10)))) = ((h4 (e11)) = (h4 (op1 (e10) (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H3f1. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H3f2. % 19.71/19.90 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3f3]. % 19.71/19.90 cut (((h4 (op1 (e10) (e10))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3f4]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e10) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H4a]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H4a zenon_H4c). % 19.71/19.90 apply zenon_H3f3. apply refl_equal. % 19.71/19.90 apply zenon_H3f3. apply refl_equal. % 19.71/19.90 cut (((op2 (e23) (e23)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3f5]. % 19.71/19.90 cut (((op2 (e23) (e23)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3f5]. % 19.71/19.90 congruence. % 19.71/19.90 apply zenon_H3f5. apply sym_equal. exact zenon_H4f. % 19.71/19.90 apply zenon_H3f5. apply sym_equal. exact zenon_H4f. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H16 | zenon_intro zenon_H4d ]. % 19.71/19.90 apply (zenon_L2_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H1d | zenon_intro zenon_H24 ]. % 19.71/19.90 apply (zenon_L3_); trivial. % 19.71/19.90 apply (zenon_L4_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H3ee); [ zenon_intro zenon_H3f7 | zenon_intro zenon_H3f6 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.71/19.90 apply (zenon_L9_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.71/19.90 apply (zenon_L10_); trivial. % 19.71/19.90 cut (((h4 (e10)) = (op2 (e23) (e23))) = ((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H3f7. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H4f. % 19.71/19.90 cut (((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3f8]. % 19.71/19.90 cut (((h4 (e10)) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3f9]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [ zenon_intro zenon_H3fa | zenon_intro zenon_H3fb ]. % 19.71/19.90 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11)))) = ((h4 (e10)) = (h4 (op1 (e10) (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H3f9. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H3fa. % 19.71/19.90 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3fb]. % 19.71/19.90 cut (((h4 (op1 (e10) (e11))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3fc]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e10) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H3fd]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H3fd zenon_H5e). % 19.71/19.90 apply zenon_H3fb. apply refl_equal. % 19.71/19.90 apply zenon_H3fb. apply refl_equal. % 19.71/19.90 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H3fe | zenon_intro zenon_H3ff ]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H3f8. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H3fe. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3ff]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H400]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e20) (e21)) = (e20)) = ((op2 (h4 (e10)) (h4 (e11))) = (op2 (e23) (e23)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H400. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H56. % 19.71/19.90 cut (((e20) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 19.71/19.90 cut (((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H401]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H3fe | zenon_intro zenon_H3ff ]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H401. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H3fe. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3ff]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H402]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 19.71/19.90 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.71/19.90 congruence. % 19.71/19.90 apply (zenon_L11_); trivial. % 19.71/19.90 apply (zenon_L12_); trivial. % 19.71/19.90 apply zenon_H3ff. apply refl_equal. % 19.71/19.90 apply zenon_H3ff. apply refl_equal. % 19.71/19.90 exact (zenon_H245 zenon_H2c). % 19.71/19.90 apply zenon_H3ff. apply refl_equal. % 19.71/19.90 apply zenon_H3ff. apply refl_equal. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H3f6); [ zenon_intro zenon_H404 | zenon_intro zenon_H403 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.71/19.90 apply (zenon_L9_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_He9 | zenon_intro zenon_H7c ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.71/19.90 apply (zenon_L10_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H14d | zenon_intro zenon_H79 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 19.71/19.90 exact (zenon_He9 zenon_Heb). % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Hec ]. % 19.71/19.90 apply (zenon_L14_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_He3 | zenon_intro zenon_H75 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H14c); [ zenon_intro zenon_H14f | zenon_intro zenon_H14e ]. % 19.71/19.90 exact (zenon_H14d zenon_H14f). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H14e); [ zenon_intro zenon_H5f | zenon_intro zenon_H150 ]. % 19.71/19.90 apply (zenon_L16_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H150); [ zenon_intro zenon_H146 | zenon_intro zenon_H6f ]. % 19.71/19.90 cut (((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H404. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H66. % 19.71/19.90 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H405]. % 19.71/19.90 cut (((h4 (e12)) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H406]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [ zenon_intro zenon_H407 | zenon_intro zenon_H408 ]. % 19.71/19.90 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12)))) = ((h4 (e12)) = (h4 (op1 (e10) (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H406. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H407. % 19.71/19.90 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H408]. % 19.71/19.90 cut (((h4 (op1 (e10) (e12))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H409]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e10) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H40a]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H40a zenon_H146). % 19.71/19.90 apply zenon_H408. apply refl_equal. % 19.71/19.90 apply zenon_H408. apply refl_equal. % 19.71/19.90 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H40b | zenon_intro zenon_H40c ]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e10)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H405. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H40b. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H40c]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H40d]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e20) (e22)) = (e22)) = ((op2 (h4 (e10)) (h4 (e12))) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H40d. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_He3. % 19.71/19.90 cut (((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H40e]. % 19.71/19.90 cut (((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H40f]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H40b | zenon_intro zenon_H40c ]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H40f. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H40b. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H40c]. % 19.71/19.90 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H410]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.71/19.90 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.71/19.90 congruence. % 19.71/19.90 apply (zenon_L11_); trivial. % 19.71/19.90 apply (zenon_L17_); trivial. % 19.71/19.90 apply zenon_H40c. apply refl_equal. % 19.71/19.90 apply zenon_H40c. apply refl_equal. % 19.71/19.90 exact (zenon_H40e zenon_H67). % 19.71/19.90 apply zenon_H40c. apply refl_equal. % 19.71/19.90 apply zenon_H40c. apply refl_equal. % 19.71/19.90 apply (zenon_L20_); trivial. % 19.71/19.90 apply (zenon_L23_); trivial. % 19.71/19.90 apply (zenon_L24_); trivial. % 19.71/19.90 apply (zenon_L25_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H403); [ zenon_intro zenon_H88 | zenon_intro zenon_H411 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H2ed); [ zenon_intro zenon_H7f | zenon_intro zenon_H412 ]. % 19.71/19.90 apply (zenon_L26_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H412); [ zenon_intro zenon_H3d | zenon_intro zenon_H413 ]. % 19.71/19.90 apply (zenon_L8_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H413); [ zenon_intro zenon_H75 | zenon_intro zenon_H8a ]. % 19.71/19.90 apply (zenon_L23_); trivial. % 19.71/19.90 apply (zenon_L29_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H411); [ zenon_intro zenon_H415 | zenon_intro zenon_H414 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3d0); [ zenon_intro zenon_H234 | zenon_intro zenon_H9c ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H154 | zenon_intro zenon_Hef ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.71/19.90 apply (zenon_L10_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3c4); [ zenon_intro zenon_H156 | zenon_intro zenon_Hf2 ]. % 19.71/19.90 apply (zenon_L67_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H9c | zenon_intro zenon_H235 ]. % 19.71/19.90 exact (zenon_H234 zenon_H9c). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H236 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H157); [ zenon_intro zenon_Hef | zenon_intro zenon_H159 ]. % 19.71/19.90 exact (zenon_H154 zenon_Hef). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H159); [ zenon_intro zenon_H12c | zenon_intro zenon_H15a ]. % 19.71/19.90 cut (((h4 (e10)) = (op2 (e23) (e23))) = ((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H415. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H4f. % 19.71/19.90 cut (((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H41a]. % 19.71/19.90 cut (((h4 (e10)) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H41b]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [ zenon_intro zenon_H41c | zenon_intro zenon_H41d ]. % 19.71/19.90 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10)))) = ((h4 (e10)) = (h4 (op1 (e11) (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H41b. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H41c. % 19.71/19.90 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H41d]. % 19.71/19.90 cut (((h4 (op1 (e11) (e10))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H41e]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e11) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H132]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H132 zenon_H12c). % 19.71/19.90 apply zenon_H41d. apply refl_equal. % 19.71/19.90 apply zenon_H41d. apply refl_equal. % 19.71/19.90 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H41f | zenon_intro zenon_H420 ]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H41a. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H41f. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H420]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H421]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e21) (e20)) = (e20)) = ((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H421. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H1b4. % 19.71/19.90 cut (((e20) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H245]. % 19.71/19.90 cut (((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H422]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H41f | zenon_intro zenon_H420 ]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H422. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H41f. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H420]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H423]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.71/19.90 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 19.71/19.90 congruence. % 19.71/19.90 apply (zenon_L12_); trivial. % 19.71/19.90 apply (zenon_L11_); trivial. % 19.71/19.90 apply zenon_H420. apply refl_equal. % 19.71/19.90 apply zenon_H420. apply refl_equal. % 19.71/19.90 exact (zenon_H245 zenon_H2c). % 19.71/19.90 apply zenon_H420. apply refl_equal. % 19.71/19.90 apply zenon_H420. apply refl_equal. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H15a); [ zenon_intro zenon_Hf3 | zenon_intro zenon_H13f ]. % 19.71/19.90 apply (zenon_L47_); trivial. % 19.71/19.90 apply (zenon_L62_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H15f | zenon_intro zenon_H162 ]. % 19.71/19.90 apply (zenon_L69_); trivial. % 19.71/19.90 apply (zenon_L70_); trivial. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H414); [ zenon_intro zenon_H425 | zenon_intro zenon_H424 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 cut (((h4 (e11)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H425. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H52. % 19.71/19.90 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H426]. % 19.71/19.90 cut (((h4 (e11)) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H427]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [ zenon_intro zenon_H428 | zenon_intro zenon_H429 ]. % 19.71/19.90 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11)))) = ((h4 (e11)) = (h4 (op1 (e11) (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H427. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H428. % 19.71/19.90 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H429]. % 19.71/19.90 cut (((h4 (op1 (e11) (e11))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H42a]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e11) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H179]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H179 zenon_Hfc). % 19.71/19.90 apply zenon_H429. apply refl_equal. % 19.71/19.90 apply zenon_H429. apply refl_equal. % 19.71/19.90 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H42b | zenon_intro zenon_H42c ]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H426. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H42b. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H42c]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H42d]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e21) (e21)) = (e21)) = ((op2 (h4 (e11)) (h4 (e11))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H42d. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_Ha7. % 19.71/19.90 cut (((e21) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 19.71/19.90 cut (((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H42e]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [ zenon_intro zenon_H42b | zenon_intro zenon_H42c ]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11)))) = ((op2 (e21) (e21)) = (op2 (h4 (e11)) (h4 (e11))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H42e. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H42b. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H42c]. % 19.71/19.90 cut (((op2 (h4 (e11)) (h4 (e11))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H42f]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 19.71/19.90 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H51]. % 19.71/19.90 congruence. % 19.71/19.90 apply (zenon_L12_); trivial. % 19.71/19.90 apply (zenon_L12_); trivial. % 19.71/19.90 apply zenon_H42c. apply refl_equal. % 19.71/19.90 apply zenon_H42c. apply refl_equal. % 19.71/19.90 exact (zenon_H266 zenon_H2e). % 19.71/19.90 apply zenon_H42c. apply refl_equal. % 19.71/19.90 apply zenon_H42c. apply refl_equal. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H424); [ zenon_intro zenon_H1d1 | zenon_intro zenon_H430 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3d0); [ zenon_intro zenon_H234 | zenon_intro zenon_H9c ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.71/19.90 apply (zenon_L9_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_He9 | zenon_intro zenon_H7c ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hce ]. % 19.71/19.90 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_H232 | zenon_intro zenon_H1f2 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H154 | zenon_intro zenon_Hef ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.71/19.90 apply (zenon_L10_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H14d | zenon_intro zenon_H79 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3c4); [ zenon_intro zenon_H156 | zenon_intro zenon_Hf2 ]. % 19.71/19.90 apply (zenon_L67_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H123 | zenon_intro zenon_H144 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H9c | zenon_intro zenon_H235 ]. % 19.71/19.90 exact (zenon_H234 zenon_H9c). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H235); [ zenon_intro zenon_H1b4 | zenon_intro zenon_H236 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_He7); [ zenon_intro zenon_Heb | zenon_intro zenon_Hea ]. % 19.71/19.90 exact (zenon_He9 zenon_Heb). % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hea); [ zenon_intro zenon_H57 | zenon_intro zenon_Hec ]. % 19.71/19.90 apply (zenon_L14_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_He3 | zenon_intro zenon_H75 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H75 | zenon_intro zenon_H239 ]. % 19.71/19.90 apply (zenon_L23_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H1c4 | zenon_intro zenon_H23a ]. % 19.71/19.90 apply (zenon_L97_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H23a); [ zenon_intro zenon_Hd1 | zenon_intro zenon_H23b ]. % 19.71/19.90 apply (zenon_L40_); trivial. % 19.71/19.90 exact (zenon_H232 zenon_H23b). % 19.71/19.90 apply (zenon_L23_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H236); [ zenon_intro zenon_H15f | zenon_intro zenon_H162 ]. % 19.71/19.90 apply (zenon_L69_); trivial. % 19.71/19.90 apply (zenon_L70_); trivial. % 19.71/19.90 apply (zenon_L63_); trivial. % 19.71/19.90 apply (zenon_L24_); trivial. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_L98_); trivial. % 19.71/19.90 apply (zenon_L25_); trivial. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H430); [ zenon_intro zenon_H1f4 | zenon_intro zenon_H431 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H153); [ zenon_intro zenon_H123 | zenon_intro zenon_H144 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H122); [ zenon_intro zenon_H6f | zenon_intro zenon_H124 ]. % 19.71/19.90 apply (zenon_L20_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H124); [ zenon_intro zenon_H107 | zenon_intro zenon_H125 ]. % 19.71/19.90 apply (zenon_L99_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H125); [ zenon_intro zenon_H11b | zenon_intro zenon_H126 ]. % 19.71/19.90 apply (zenon_L55_); trivial. % 19.71/19.90 exact (zenon_H123 zenon_H126). % 19.71/19.90 apply (zenon_L63_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H431); [ zenon_intro zenon_H433 | zenon_intro zenon_H432 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H154 | zenon_intro zenon_Hef ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.71/19.90 apply (zenon_L10_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3c4); [ zenon_intro zenon_H156 | zenon_intro zenon_Hf2 ]. % 19.71/19.90 apply (zenon_L67_); trivial. % 19.71/19.90 cut (((h4 (e12)) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23))) = ((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H433. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H66. % 19.71/19.90 cut (((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H434]. % 19.71/19.90 cut (((h4 (e12)) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H435]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [ zenon_intro zenon_H436 | zenon_intro zenon_H437 ]. % 19.71/19.90 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10)))) = ((h4 (e12)) = (h4 (op1 (e12) (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H435. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H436. % 19.71/19.90 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H437]. % 19.71/19.90 cut (((h4 (op1 (e12) (e10))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H438]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H439]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H439 zenon_Hf2). % 19.71/19.90 apply zenon_H437. apply refl_equal. % 19.71/19.90 apply zenon_H437. apply refl_equal. % 19.71/19.90 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H43a | zenon_intro zenon_H43b ]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)) = (op2 (h4 (e12)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H434. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H43a. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H43b]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H43c]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e22) (e20)) = (e22)) = ((op2 (h4 (e12)) (h4 (e10))) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H43c. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H15e. % 19.71/19.90 cut (((e22) = (op2 (op2 (op2 (e23) (e23)) (op2 (e23) (e23))) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H40e]. % 19.71/19.90 cut (((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H43d]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H43a | zenon_intro zenon_H43b ]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H43d. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H43a. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H43b]. % 19.71/19.90 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H43e]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.71/19.90 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H65]. % 19.71/19.90 congruence. % 19.71/19.90 apply (zenon_L17_); trivial. % 19.71/19.90 apply (zenon_L11_); trivial. % 19.71/19.90 apply zenon_H43b. apply refl_equal. % 19.71/19.90 apply zenon_H43b. apply refl_equal. % 19.71/19.90 exact (zenon_H40e zenon_H67). % 19.71/19.90 apply zenon_H43b. apply refl_equal. % 19.71/19.90 apply zenon_H43b. apply refl_equal. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H432); [ zenon_intro zenon_H214 | zenon_intro zenon_H43f ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3d0); [ zenon_intro zenon_H234 | zenon_intro zenon_H9c ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.71/19.90 apply (zenon_L9_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1c1 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hce ]. % 19.71/19.90 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3e3); [ zenon_intro zenon_H232 | zenon_intro zenon_H1f2 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H154 | zenon_intro zenon_Hef ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.71/19.90 apply (zenon_L10_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3c1); [ zenon_intro zenon_H18a | zenon_intro zenon_H1ce ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H127 | zenon_intro zenon_H12b ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H128); [ zenon_intro zenon_Hf2 | zenon_intro zenon_H129 ]. % 19.71/19.90 apply (zenon_L110_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H129); [ zenon_intro zenon_H10e | zenon_intro zenon_H12a ]. % 19.71/19.90 apply (zenon_L111_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H12a); [ zenon_intro zenon_H12b | zenon_intro zenon_H11b ]. % 19.71/19.90 exact (zenon_H127 zenon_H12b). % 19.71/19.90 apply (zenon_L55_); trivial. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L92_); trivial. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_L98_); trivial. % 19.71/19.90 apply (zenon_L89_); trivial. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H43f); [ zenon_intro zenon_H23c | zenon_intro zenon_H440 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3d0); [ zenon_intro zenon_H234 | zenon_intro zenon_H9c ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.71/19.90 apply (zenon_L9_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_H4a | zenon_intro zenon_H5e ]. % 19.71/19.90 apply (zenon_L10_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H151); [ zenon_intro zenon_H14d | zenon_intro zenon_H79 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3c6); [ zenon_intro zenon_H24e | zenon_intro zenon_H10e ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H152); [ zenon_intro zenon_H127 | zenon_intro zenon_H12b ]. % 19.71/19.90 apply (zenon_L114_); trivial. % 19.71/19.90 apply (zenon_L65_); trivial. % 19.71/19.90 apply (zenon_L111_); trivial. % 19.71/19.90 apply (zenon_L24_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H440); [ zenon_intro zenon_H25d | zenon_intro zenon_H441 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3dd); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H1fe ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3cb); [ zenon_intro zenon_H17a | zenon_intro zenon_H115 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H44); [ zenon_intro zenon_H47 | zenon_intro zenon_H46 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H318); [ zenon_intro zenon_H257 | zenon_intro zenon_H442 ]. % 19.71/19.90 apply (zenon_L115_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H442); [ zenon_intro zenon_H20a | zenon_intro zenon_H443 ]. % 19.71/19.90 apply (zenon_L103_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H443); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hb8 ]. % 19.71/19.90 exact (zenon_Hc3 zenon_Hbf). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H17b); [ zenon_intro zenon_H24 | zenon_intro zenon_H17c ]. % 19.71/19.90 apply (zenon_L4_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H17c); [ zenon_intro zenon_H168 | zenon_intro zenon_H17d ]. % 19.71/19.90 apply (zenon_L116_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H17d); [ zenon_intro zenon_H16e | zenon_intro zenon_H173 ]. % 19.71/19.90 apply (zenon_L117_); trivial. % 19.71/19.90 exact (zenon_H17a zenon_H173). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H46); [ zenon_intro zenon_H2f | zenon_intro zenon_H48 ]. % 19.71/19.90 apply (zenon_L6_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H48); [ zenon_intro zenon_H36 | zenon_intro zenon_H3d ]. % 19.71/19.90 apply (zenon_L7_); trivial. % 19.71/19.90 apply (zenon_L8_); trivial. % 19.71/19.90 apply (zenon_L53_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_L100_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H441); [ zenon_intro zenon_H445 | zenon_intro zenon_H444 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_Hdc); [ zenon_intro zenon_H2d | zenon_intro zenon_Hce ]. % 19.71/19.90 apply zenon_H2d. apply sym_equal. exact zenon_H2c. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H446 | zenon_intro zenon_H447 ]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H445. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H446. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H447]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H448]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (h4 (e13)) (h4 (e10))) = (h4 (op1 (e13) (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H448. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_Hce. % 19.71/19.90 cut (((e23) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 19.71/19.90 cut (((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H449]. % 19.71/19.90 congruence. % 19.71/19.90 elim (classic ((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [ zenon_intro zenon_H446 | zenon_intro zenon_H447 ]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10)))) = ((op2 (e23) (e20)) = (op2 (h4 (e13)) (h4 (e10))))). % 19.71/19.90 intro zenon_D_pnotp. % 19.71/19.90 apply zenon_H449. % 19.71/19.90 rewrite <- zenon_D_pnotp. % 19.71/19.90 exact zenon_H446. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H447]. % 19.71/19.90 cut (((op2 (h4 (e13)) (h4 (e10))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H44a]. % 19.71/19.90 congruence. % 19.71/19.90 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H4e]. % 19.71/19.90 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 19.71/19.90 congruence. % 19.71/19.90 exact (zenon_H97 zenon_H8b). % 19.71/19.90 apply (zenon_L11_); trivial. % 19.71/19.90 apply zenon_H447. apply refl_equal. % 19.71/19.90 apply zenon_H447. apply refl_equal. % 19.71/19.90 apply (zenon_L118_); trivial. % 19.71/19.90 apply zenon_H447. apply refl_equal. % 19.71/19.90 apply zenon_H447. apply refl_equal. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H444); [ zenon_intro zenon_H277 | zenon_intro zenon_H44b ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H9b); [ zenon_intro zenon_H45 | zenon_intro zenon_H56 ]. % 19.71/19.90 apply (zenon_L9_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3d8); [ zenon_intro zenon_H1ab | zenon_intro zenon_H1c1 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H231); [ zenon_intro zenon_H57 | zenon_intro zenon_H237 ]. % 19.71/19.90 apply (zenon_L14_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H237); [ zenon_intro zenon_H1a9 | zenon_intro zenon_H238 ]. % 19.71/19.90 exact (zenon_H1ab zenon_H1a9). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H238); [ zenon_intro zenon_H1fe | zenon_intro zenon_H210 ]. % 19.71/19.90 apply (zenon_L100_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H118); [ zenon_intro zenon_Hf6 | zenon_intro zenon_H119 ]. % 19.71/19.90 apply (zenon_L48_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H119); [ zenon_intro zenon_H101 | zenon_intro zenon_H11a ]. % 19.71/19.90 apply (zenon_L50_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H11a); [ zenon_intro zenon_H108 | zenon_intro zenon_H115 ]. % 19.71/19.90 apply (zenon_L120_); trivial. % 19.71/19.90 apply (zenon_L53_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H16 | zenon_intro zenon_H4d ]. % 19.71/19.90 apply (zenon_L2_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H1d | zenon_intro zenon_H24 ]. % 19.71/19.90 apply (zenon_L3_); trivial. % 19.71/19.90 apply (zenon_L4_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_L89_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H44b); [ zenon_intro zenon_H28a | zenon_intro zenon_H44c ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3ce); [ zenon_intro zenon_H9c | zenon_intro zenon_H416 ]. % 19.71/19.90 apply (zenon_L30_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H416); [ zenon_intro zenon_Ha7 | zenon_intro zenon_H417 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3db); [ zenon_intro zenon_Hc5 | zenon_intro zenon_H15e ]. % 19.71/19.90 apply (zenon_L44_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3dd); [ zenon_intro zenon_Hc3 | zenon_intro zenon_H1fe ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3b7); [ zenon_intro zenon_Hef | zenon_intro zenon_H418 ]. % 19.71/19.90 apply (zenon_L45_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H418); [ zenon_intro zenon_Hfc | zenon_intro zenon_H419 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H158); [ zenon_intro zenon_H14 | zenon_intro zenon_H114 ]. % 19.71/19.90 apply zenon_H14. apply sym_equal. exact zenon_H13. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H3cb); [ zenon_intro zenon_H17a | zenon_intro zenon_H115 ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H31a); [ zenon_intro zenon_H36 | zenon_intro zenon_H44d ]. % 19.71/19.90 apply (zenon_L7_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H44d); [ zenon_intro zenon_H1c1 | zenon_intro zenon_H44e ]. % 19.71/19.90 apply (zenon_L89_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H44e); [ zenon_intro zenon_Hbf | zenon_intro zenon_Hbb ]. % 19.71/19.90 exact (zenon_Hc3 zenon_Hbf). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H49); [ zenon_intro zenon_H4c | zenon_intro zenon_H4b ]. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H27d | zenon_intro zenon_H44f ]. % 19.71/19.90 apply (zenon_L121_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H44f); [ zenon_intro zenon_H101 | zenon_intro zenon_H450 ]. % 19.71/19.90 apply (zenon_L50_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H450); [ zenon_intro zenon_H282 | zenon_intro zenon_H173 ]. % 19.71/19.90 apply (zenon_L123_); trivial. % 19.71/19.90 exact (zenon_H17a zenon_H173). % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4b); [ zenon_intro zenon_H16 | zenon_intro zenon_H4d ]. % 19.71/19.90 apply (zenon_L2_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H4d); [ zenon_intro zenon_H1d | zenon_intro zenon_H24 ]. % 19.71/19.90 apply (zenon_L3_); trivial. % 19.71/19.90 apply (zenon_L4_); trivial. % 19.71/19.90 apply (zenon_L53_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H419); [ zenon_intro zenon_H12b | zenon_intro zenon_H166 ]. % 19.71/19.90 apply (zenon_L66_); trivial. % 19.71/19.90 apply (zenon_L78_); trivial. % 19.71/19.90 apply (zenon_L100_); trivial. % 19.71/19.90 apply (zenon_or_s _ _ zenon_H417); [ zenon_intro zenon_Hcc | zenon_intro zenon_H192 ]. % 19.71/19.90 apply (zenon_L43_); trivial. % 19.71/19.90 apply (zenon_L86_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H44c); [ zenon_intro zenon_H290 | zenon_intro zenon_H451 ]. % 19.71/19.90 apply (zenon_L124_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H451); [ zenon_intro zenon_H453 | zenon_intro zenon_H452 ]. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H453). zenon_intro zenon_H4e. zenon_intro zenon_H454. % 19.71/19.90 apply (zenon_L11_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H452); [ zenon_intro zenon_H456 | zenon_intro zenon_H455 ]. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H456). zenon_intro zenon_H458. zenon_intro zenon_H457. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H457). zenon_intro zenon_H51. zenon_intro zenon_H459. % 19.71/19.90 apply (zenon_L12_); trivial. % 19.71/19.90 apply (zenon_notand_s _ _ zenon_H455); [ zenon_intro zenon_H45a | zenon_intro zenon_H296 ]. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H45a). zenon_intro zenon_H45c. zenon_intro zenon_H45b. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H45b). zenon_intro zenon_H45e. zenon_intro zenon_H45d. % 19.71/19.90 apply (zenon_notor_s _ _ zenon_H45d). zenon_intro zenon_H65. zenon_intro zenon_H45f. % 19.71/19.90 apply (zenon_L17_); trivial. % 19.71/19.90 apply (zenon_L125_); trivial. % 19.71/19.90 Qed. % 19.71/19.90 % SZS output end Proof % 19.71/19.90 (* END-PROOF *) % 19.71/19.90 nodes searched: 1202477 % 19.71/19.90 max branch formulas: 1847 % 19.71/19.90 proof nodes created: 10423 % 19.71/19.90 formulas created: 483365 % 19.71/19.90 %------------------------------------------------------------------------------