%------------------------------------------------------------------------------ % File : Zenon---0.7.1 % Problem : ALG125+1 : TPTP v8.1.0. Released v2.7.0. % Transfm : none % Format : tptp:raw % Command : run_zenon %s %d % Computer : n021.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 18:29:35 EDT 2022 % Result : Theorem 32.93s 33.13s % Output : Proof 33.05s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.12/0.13 % Problem : ALG125+1 : TPTP v8.1.0. Released v2.7.0. % 0.12/0.13 % Command : run_zenon %s %d % 0.13/0.35 % Computer : n021.cluster.edu % 0.13/0.35 % Model : x86_64 x86_64 % 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.35 % Memory : 8042.1875MB % 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.35 % CPULimit : 300 % 0.13/0.35 % WCLimit : 600 % 0.13/0.35 % DateTime : Thu Jun 9 05:46:23 EDT 2022 % 0.13/0.35 % CPUTime : % 32.93/33.13 (* PROOF-FOUND *) % 32.93/33.13 % SZS status Theorem % 32.93/33.13 (* BEGIN-PROOF *) % 32.93/33.13 % SZS output start Proof % 32.93/33.13 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))))))))))))))))))))))))))). % 32.93/33.13 Proof. % 32.93/33.13 assert (zenon_L1_ : (~((e20) = (e20))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H12. % 32.93/33.13 apply zenon_H12. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L1_ *) % 32.93/33.13 assert (zenon_L2_ : (~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> False). % 32.93/33.13 do 0 intro. intros zenon_H13 zenon_H14. % 32.93/33.13 cut (((op2 (e20) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H15]. % 32.93/33.13 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H12. apply refl_equal. % 32.93/33.13 exact (zenon_H15 zenon_H14). % 32.93/33.13 (* end of lemma zenon_L2_ *) % 32.93/33.13 assert (zenon_L3_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H16 zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 32.93/33.13 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H18. apply sym_equal. exact zenon_H17. % 32.93/33.13 apply zenon_H18. apply sym_equal. exact zenon_H17. % 32.93/33.13 (* end of lemma zenon_L3_ *) % 32.93/33.13 assert (zenon_L4_ : (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H19 zenon_H1a zenon_H1b zenon_H17. % 32.93/33.13 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e20) (e21)) = (op2 (e21) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H19. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H1a. % 32.93/33.13 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 32.93/33.13 cut (((e20) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1c]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ]. % 32.93/33.13 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e20) = (op2 (e20) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H1c. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H1d. % 32.93/33.13 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 32.93/33.13 cut (((op2 (e20) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H1f]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H1f zenon_H1b). % 32.93/33.13 apply zenon_H1e. apply refl_equal. % 32.93/33.13 apply zenon_H1e. apply refl_equal. % 32.93/33.13 apply (zenon_L3_); trivial. % 32.93/33.13 (* end of lemma zenon_L4_ *) % 32.93/33.13 assert (zenon_L5_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H1a zenon_H20 zenon_H17 zenon_H21. % 32.93/33.13 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 32.93/33.13 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((op2 (e21) (e21)) = (op2 (e22) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H21. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H22. % 32.93/33.13 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 32.93/33.13 cut (((op2 (e22) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H24]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e22) (e21)) = (op2 (e21) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H24. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H1a. % 32.93/33.13 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 32.93/33.13 cut (((e20) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H25]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 32.93/33.13 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e20) = (op2 (e22) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H25. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H22. % 32.93/33.13 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 32.93/33.13 cut (((op2 (e22) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H26]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H26 zenon_H20). % 32.93/33.13 apply zenon_H23. apply refl_equal. % 32.93/33.13 apply zenon_H23. apply refl_equal. % 32.93/33.13 apply (zenon_L3_); trivial. % 32.93/33.13 apply zenon_H23. apply refl_equal. % 32.93/33.13 apply zenon_H23. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L5_ *) % 32.93/33.13 assert (zenon_L6_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e23) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H1a zenon_H27 zenon_H17 zenon_H28. % 32.93/33.13 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H29 | zenon_intro zenon_H2a ]. % 32.93/33.13 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e21) (e21)) = (op2 (e23) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H28. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H29. % 32.93/33.13 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 32.93/33.13 cut (((op2 (e23) (e21)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2b]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e23) (e21)) = (op2 (e21) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H2b. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H1a. % 32.93/33.13 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 32.93/33.13 cut (((e20) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2c]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H29 | zenon_intro zenon_H2a ]. % 32.93/33.13 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e20) = (op2 (e23) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H2c. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H29. % 32.93/33.13 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 32.93/33.13 cut (((op2 (e23) (e21)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2d]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H2d zenon_H27). % 32.93/33.13 apply zenon_H2a. apply refl_equal. % 32.93/33.13 apply zenon_H2a. apply refl_equal. % 32.93/33.13 apply (zenon_L3_); trivial. % 32.93/33.13 apply zenon_H2a. apply refl_equal. % 32.93/33.13 apply zenon_H2a. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L6_ *) % 32.93/33.13 assert (zenon_L7_ : (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e21)) = (e20))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H2e zenon_H19 zenon_H2f zenon_H21 zenon_H1a zenon_H17 zenon_H28. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H1b | zenon_intro zenon_H30 ]. % 32.93/33.13 apply (zenon_L4_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 32.93/33.13 exact (zenon_H2f zenon_H32). % 32.93/33.13 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H20 | zenon_intro zenon_H27 ]. % 32.93/33.13 apply (zenon_L5_); trivial. % 32.93/33.13 apply (zenon_L6_); trivial. % 32.93/33.13 (* end of lemma zenon_L7_ *) % 32.93/33.13 assert (zenon_L8_ : (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e21) (e21)) = (e21)) -> False). % 32.93/33.13 do 0 intro. intros zenon_H33 zenon_H34 zenon_H35. % 32.93/33.13 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (e21) (e20)) = (op2 (e21) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H33. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H34. % 32.93/33.13 cut (((e21) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H36]. % 32.93/33.13 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H37. apply refl_equal. % 32.93/33.13 apply zenon_H36. apply sym_equal. exact zenon_H35. % 32.93/33.13 (* end of lemma zenon_L8_ *) % 32.93/33.13 assert (zenon_L9_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((op2 (e21) (e21)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H38 zenon_H35 zenon_H33 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 32.93/33.13 apply (zenon_L7_); trivial. % 32.93/33.13 apply (zenon_L8_); trivial. % 32.93/33.13 (* end of lemma zenon_L9_ *) % 32.93/33.13 assert (zenon_L10_ : ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e23) (e23)) = (op2 (e21) (e20)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H17 zenon_H34 zenon_H39. % 32.93/33.13 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H37 ]. % 32.93/33.13 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((op2 (e23) (e23)) = (op2 (e21) (e20)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H39. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H3a. % 32.93/33.13 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 32.93/33.13 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H3b. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 32.93/33.13 cut (((e21) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H37 ]. % 32.93/33.13 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e21) = (op2 (e21) (e20)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H3d. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H3a. % 32.93/33.13 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 32.93/33.13 cut (((op2 (e21) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H3e zenon_H34). % 32.93/33.13 apply zenon_H37. apply refl_equal. % 32.93/33.13 apply zenon_H37. apply refl_equal. % 32.93/33.13 apply zenon_H3c. apply refl_equal. % 32.93/33.13 apply zenon_H37. apply refl_equal. % 32.93/33.13 apply zenon_H37. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L10_ *) % 32.93/33.13 assert (zenon_L11_ : ((op2 (e22) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H3f zenon_H17 zenon_H34 zenon_H40. % 32.93/33.13 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H42 ]. % 32.93/33.13 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((op2 (e21) (e20)) = (op2 (e22) (e20)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H40. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H41. % 32.93/33.13 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 32.93/33.13 cut (((op2 (e22) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H43]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e20)) = (op2 (e21) (e20)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H43. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 32.93/33.13 cut (((e21) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H44]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H42 ]. % 32.93/33.13 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e21) = (op2 (e22) (e20)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H44. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H41. % 32.93/33.13 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 32.93/33.13 cut (((op2 (e22) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H45]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H45 zenon_H3f). % 32.93/33.13 apply zenon_H42. apply refl_equal. % 32.93/33.13 apply zenon_H42. apply refl_equal. % 32.93/33.13 apply (zenon_L10_); trivial. % 32.93/33.13 apply zenon_H42. apply refl_equal. % 32.93/33.13 apply zenon_H42. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L11_ *) % 32.93/33.13 assert (zenon_L12_ : (~((op2 (e23) (e23)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e21)) = (e21)) -> False). % 32.93/33.13 do 0 intro. intros zenon_H46 zenon_H34 zenon_H17 zenon_H47. % 32.93/33.13 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (e23) (e23)) = (op2 (e22) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H46. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H34. % 32.93/33.13 cut (((e21) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H48]. % 32.93/33.13 cut (((op2 (e21) (e20)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3b]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H49 | zenon_intro zenon_H3c ]. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e21) (e20)) = (op2 (e23) (e23)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H3b. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H49. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H39]. % 32.93/33.13 congruence. % 32.93/33.13 apply (zenon_L10_); trivial. % 32.93/33.13 apply zenon_H3c. apply refl_equal. % 32.93/33.13 apply zenon_H3c. apply refl_equal. % 32.93/33.13 apply zenon_H48. apply sym_equal. exact zenon_H47. % 32.93/33.13 (* end of lemma zenon_L12_ *) % 32.93/33.13 assert (zenon_L13_ : (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e21)) = (e21)) -> ((op2 (e22) (e21)) = (e21)) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H4a zenon_H4b zenon_H47 zenon_H34 zenon_H17. % 32.93/33.13 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H4a. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 32.93/33.13 cut (((e21) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H4c]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e20) (e21)) = (op2 (e20) (e21)))); [ zenon_intro zenon_H1d | zenon_intro zenon_H1e ]. % 32.93/33.13 cut (((op2 (e20) (e21)) = (op2 (e20) (e21))) = ((e21) = (op2 (e20) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H4c. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H1d. % 32.93/33.13 cut (((op2 (e20) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1e]. % 32.93/33.13 cut (((op2 (e20) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H4d]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H4d zenon_H4b). % 32.93/33.13 apply zenon_H1e. apply refl_equal. % 32.93/33.13 apply zenon_H1e. apply refl_equal. % 32.93/33.13 apply (zenon_L12_); trivial. % 32.93/33.13 (* end of lemma zenon_L13_ *) % 32.93/33.13 assert (zenon_L14_ : (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e21)) -> False). % 32.93/33.13 do 0 intro. intros zenon_H4e zenon_H17 zenon_H4f. % 32.93/33.13 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e23)) = (op2 (e23) (e23)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H4e. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 32.93/33.13 cut (((e21) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H50]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H51 | zenon_intro zenon_H52 ]. % 32.93/33.13 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e21) = (op2 (e22) (e23)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H50. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H51. % 32.93/33.13 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 32.93/33.13 cut (((op2 (e22) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H53]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H53 zenon_H4f). % 32.93/33.13 apply zenon_H52. apply refl_equal. % 32.93/33.13 apply zenon_H52. apply refl_equal. % 32.93/33.13 apply zenon_H3c. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L14_ *) % 32.93/33.13 assert (zenon_L15_ : (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H54 zenon_H40 zenon_H34 zenon_H4b zenon_H4a zenon_H55 zenon_H4e zenon_H17. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H3f | zenon_intro zenon_H56 ]. % 32.93/33.13 apply (zenon_L11_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H47 | zenon_intro zenon_H57 ]. % 32.93/33.13 apply (zenon_L13_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H4f ]. % 32.93/33.13 exact (zenon_H55 zenon_H58). % 32.93/33.13 apply (zenon_L14_); trivial. % 32.93/33.13 (* end of lemma zenon_L15_ *) % 32.93/33.13 assert (zenon_L16_ : (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e20) (e21)) = (e21)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e22)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H54 zenon_H40 zenon_H34 zenon_H4b zenon_H4a zenon_H59 zenon_H5a zenon_H4e zenon_H17. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H54); [ zenon_intro zenon_H3f | zenon_intro zenon_H56 ]. % 32.93/33.13 apply (zenon_L11_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H56); [ zenon_intro zenon_H47 | zenon_intro zenon_H57 ]. % 32.93/33.13 apply (zenon_L13_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H57); [ zenon_intro zenon_H58 | zenon_intro zenon_H4f ]. % 32.93/33.13 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H5a. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H59. % 32.93/33.13 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 32.93/33.13 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H5c. apply refl_equal. % 32.93/33.13 apply zenon_H5b. apply sym_equal. exact zenon_H58. % 32.93/33.13 apply (zenon_L14_); trivial. % 32.93/33.13 (* end of lemma zenon_L16_ *) % 32.93/33.13 assert (zenon_L17_ : (~((e22) = (e22))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H5d. % 32.93/33.13 apply zenon_H5d. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L17_ *) % 32.93/33.13 assert (zenon_L18_ : (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e21)) = (e21)) -> False). % 32.93/33.13 do 0 intro. intros zenon_H5e zenon_H17 zenon_H5f. % 32.93/33.13 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e21)) = (op2 (e23) (e23)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H5e. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 32.93/33.13 cut (((e21) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H60]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H29 | zenon_intro zenon_H2a ]. % 32.93/33.13 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e21) = (op2 (e23) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H60. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H29. % 32.93/33.13 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 32.93/33.13 cut (((op2 (e23) (e21)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H61]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H61 zenon_H5f). % 32.93/33.13 apply zenon_H2a. apply refl_equal. % 32.93/33.13 apply zenon_H2a. apply refl_equal. % 32.93/33.13 apply zenon_H3c. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L18_ *) % 32.93/33.13 assert (zenon_L19_ : (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e23)) = (e21)) -> False). % 32.93/33.13 do 0 intro. intros zenon_H62 zenon_H17 zenon_H63. % 32.93/33.13 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e20) (e23)) = (op2 (e23) (e23)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H62. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 32.93/33.13 cut (((e21) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H64]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ]. % 32.93/33.13 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e21) = (op2 (e20) (e23)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H64. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H65. % 32.93/33.13 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 32.93/33.13 cut (((op2 (e20) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H67]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H67 zenon_H63). % 32.93/33.13 apply zenon_H66. apply refl_equal. % 32.93/33.13 apply zenon_H66. apply refl_equal. % 32.93/33.13 apply zenon_H3c. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L19_ *) % 32.93/33.13 assert (zenon_L20_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H68 zenon_H69 zenon_H6a. % 32.93/33.13 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.13 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e22) (e21)) = (op2 (e22) (e22)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H6a. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H6b. % 32.93/33.13 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.13 cut (((op2 (e22) (e22)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H6d]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e22) (e21)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H6d. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H68. % 32.93/33.13 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 32.93/33.13 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H6c. apply refl_equal. % 32.93/33.13 apply zenon_H6e. apply sym_equal. exact zenon_H69. % 32.93/33.13 apply zenon_H6c. apply refl_equal. % 32.93/33.13 apply zenon_H6c. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L20_ *) % 32.93/33.13 assert (zenon_L21_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H6f zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H70 zenon_H33 zenon_H71 zenon_H62 zenon_H5a zenon_H72 zenon_H5e zenon_H73 zenon_H40 zenon_H4a zenon_H4e zenon_H54 zenon_H6a zenon_H68 zenon_H74 zenon_H38. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 32.93/33.13 apply (zenon_L7_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H55 | zenon_intro zenon_H69 ]. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 32.93/33.13 exact (zenon_H75 zenon_H78). % 32.93/33.13 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H4b | zenon_intro zenon_H79 ]. % 32.93/33.13 apply (zenon_L15_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H59 | zenon_intro zenon_H63 ]. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H4b | zenon_intro zenon_H7a ]. % 32.93/33.13 apply (zenon_L16_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H7a); [ zenon_intro zenon_H35 | zenon_intro zenon_H7b ]. % 32.93/33.13 exact (zenon_H76 zenon_H35). % 32.93/33.13 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H47 | zenon_intro zenon_H5f ]. % 32.93/33.13 cut (((op2 (e22) (e21)) = (e21)) = ((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H72. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H47. % 32.93/33.13 cut (((e21) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 32.93/33.13 cut (((op2 (e22) (e21)) = (op2 (e22) (op2 (e20) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H7d]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op2 (e22) (op2 (e20) (e22))) = (op2 (e22) (op2 (e20) (e22))))); [ zenon_intro zenon_H7e | zenon_intro zenon_H7f ]. % 32.93/33.13 cut (((op2 (e22) (op2 (e20) (e22))) = (op2 (e22) (op2 (e20) (e22)))) = ((op2 (e22) (e21)) = (op2 (e22) (op2 (e20) (e22))))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H7d. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H7e. % 32.93/33.13 cut (((op2 (e22) (op2 (e20) (e22))) = (op2 (e22) (op2 (e20) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H7f]. % 32.93/33.13 cut (((op2 (e22) (op2 (e20) (e22))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H80]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((op2 (e20) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H81]. % 32.93/33.13 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H5d. apply refl_equal. % 32.93/33.13 exact (zenon_H81 zenon_H59). % 32.93/33.13 apply zenon_H7f. apply refl_equal. % 32.93/33.13 apply zenon_H7f. apply refl_equal. % 32.93/33.13 apply zenon_H7c. apply sym_equal. exact zenon_H59. % 32.93/33.13 apply (zenon_L18_); trivial. % 32.93/33.13 apply (zenon_L19_); trivial. % 32.93/33.13 apply (zenon_L20_); trivial. % 32.93/33.13 apply (zenon_L8_); trivial. % 32.93/33.13 apply (zenon_L4_); trivial. % 32.93/33.13 (* end of lemma zenon_L21_ *) % 32.93/33.13 assert (zenon_L22_ : (~((e21) = (e21))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H82. % 32.93/33.13 apply zenon_H82. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L22_ *) % 32.93/33.13 assert (zenon_L23_ : (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e23)) = (e23)) -> False). % 32.93/33.13 do 0 intro. intros zenon_H83 zenon_H17 zenon_H84. % 32.93/33.13 cut (((e21) = (op2 (e23) (e23))) = ((e21) = (e23))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H83. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H17. % 32.93/33.13 cut (((op2 (e23) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 32.93/33.13 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H82. apply refl_equal. % 32.93/33.13 exact (zenon_H85 zenon_H84). % 32.93/33.13 (* end of lemma zenon_L23_ *) % 32.93/33.13 assert (zenon_L24_ : ((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H86 zenon_H87 zenon_H38 zenon_H74 zenon_H6a zenon_H54 zenon_H4e zenon_H4a zenon_H40 zenon_H73 zenon_H5e zenon_H5a zenon_H62 zenon_H71 zenon_H33 zenon_H70 zenon_H19 zenon_H1a zenon_H21 zenon_H28 zenon_H2e zenon_H6f zenon_H83 zenon_H17. % 32.93/33.13 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H13. zenon_intro zenon_H88. % 32.93/33.13 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 32.93/33.13 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H72. zenon_intro zenon_H8b. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 32.93/33.13 apply (zenon_L2_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 32.93/33.13 apply (zenon_L9_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 32.93/33.13 apply (zenon_L21_); trivial. % 32.93/33.13 apply (zenon_L23_); trivial. % 32.93/33.13 (* end of lemma zenon_L24_ *) % 32.93/33.13 assert (zenon_L25_ : (~((e10) = (e10))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H8e. % 32.93/33.13 apply zenon_H8e. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L25_ *) % 32.93/33.13 assert (zenon_L26_ : (~((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H8f zenon_H90. % 32.93/33.13 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 32.93/33.13 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.13 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.13 (* end of lemma zenon_L26_ *) % 32.93/33.13 assert (zenon_L27_ : (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e10) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H92 zenon_H93 zenon_H94 zenon_H90. % 32.93/33.13 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e10) (e11)) = (op1 (e11) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H92. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H93. % 32.93/33.13 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 32.93/33.13 cut (((e10) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H95]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 32.93/33.13 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e10) = (op1 (e10) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H95. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H96. % 32.93/33.13 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 32.93/33.13 cut (((op1 (e10) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H98]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H98 zenon_H94). % 32.93/33.13 apply zenon_H97. apply refl_equal. % 32.93/33.13 apply zenon_H97. apply refl_equal. % 32.93/33.13 apply (zenon_L26_); trivial. % 32.93/33.13 (* end of lemma zenon_L27_ *) % 32.93/33.13 assert (zenon_L28_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e12) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H93 zenon_H99 zenon_H90 zenon_H9a. % 32.93/33.13 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 32.93/33.13 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e11) (e11)) = (op1 (e12) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H9a. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H9b. % 32.93/33.13 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 32.93/33.13 cut (((op1 (e12) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H9d]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e12) (e11)) = (op1 (e11) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H9d. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H93. % 32.93/33.13 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 32.93/33.13 cut (((e10) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H9e]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 32.93/33.13 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e10) = (op1 (e12) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_H9e. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H9b. % 32.93/33.13 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 32.93/33.13 cut (((op1 (e12) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H9f]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_H9f zenon_H99). % 32.93/33.13 apply zenon_H9c. apply refl_equal. % 32.93/33.13 apply zenon_H9c. apply refl_equal. % 32.93/33.13 apply (zenon_L26_); trivial. % 32.93/33.13 apply zenon_H9c. apply refl_equal. % 32.93/33.13 apply zenon_H9c. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L28_ *) % 32.93/33.13 assert (zenon_L29_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_H93 zenon_Ha0 zenon_H90 zenon_Ha1. % 32.93/33.13 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 32.93/33.13 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e11) (e11)) = (op1 (e13) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_Ha1. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_Ha2. % 32.93/33.13 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 32.93/33.13 cut (((op1 (e13) (e11)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha4]. % 32.93/33.13 congruence. % 32.93/33.13 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e13) (e11)) = (op1 (e11) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_Ha4. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_H93. % 32.93/33.13 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 32.93/33.13 cut (((e10) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha5]. % 32.93/33.13 congruence. % 32.93/33.13 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 32.93/33.13 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e10) = (op1 (e13) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_Ha5. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_Ha2. % 32.93/33.13 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 32.93/33.13 cut (((op1 (e13) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha6]. % 32.93/33.13 congruence. % 32.93/33.13 exact (zenon_Ha6 zenon_Ha0). % 32.93/33.13 apply zenon_Ha3. apply refl_equal. % 32.93/33.13 apply zenon_Ha3. apply refl_equal. % 32.93/33.13 apply (zenon_L26_); trivial. % 32.93/33.13 apply zenon_Ha3. apply refl_equal. % 32.93/33.13 apply zenon_Ha3. apply refl_equal. % 32.93/33.13 (* end of lemma zenon_L29_ *) % 32.93/33.13 assert (zenon_L30_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 32.93/33.13 do 0 intro. intros zenon_Ha7 zenon_H92 zenon_Ha8 zenon_H9a zenon_H93 zenon_H90 zenon_Ha1. % 32.93/33.13 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H94 | zenon_intro zenon_Ha9 ]. % 32.93/33.13 apply (zenon_L27_); trivial. % 32.93/33.13 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 32.93/33.13 exact (zenon_Ha8 zenon_Hab). % 32.93/33.13 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H99 | zenon_intro zenon_Ha0 ]. % 32.93/33.13 apply (zenon_L28_); trivial. % 32.93/33.13 apply (zenon_L29_); trivial. % 32.93/33.13 (* end of lemma zenon_L30_ *) % 32.93/33.13 assert (zenon_L31_ : (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e11)) = (e11)) -> False). % 32.93/33.13 do 0 intro. intros zenon_Hac zenon_Had zenon_Hae. % 32.93/33.13 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e11) (e10)) = (op1 (e11) (e11)))). % 32.93/33.13 intro zenon_D_pnotp. % 32.93/33.13 apply zenon_Hac. % 32.93/33.13 rewrite <- zenon_D_pnotp. % 32.93/33.13 exact zenon_Had. % 32.93/33.13 cut (((e11) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Haf]. % 32.93/33.13 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 32.93/33.13 congruence. % 32.93/33.13 apply zenon_Hb0. apply refl_equal. % 32.93/33.13 apply zenon_Haf. apply sym_equal. exact zenon_Hae. % 32.93/33.13 (* end of lemma zenon_L31_ *) % 32.93/33.13 assert (zenon_L32_ : ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((op1 (e11) (e11)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hb1 zenon_Hae zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.14 apply (zenon_L30_); trivial. % 32.93/33.14 apply (zenon_L31_); trivial. % 32.93/33.14 (* end of lemma zenon_L32_ *) % 32.93/33.14 assert (zenon_L33_ : ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e13) (e13)) = (op1 (e11) (e10)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H90 zenon_Had zenon_Hb2. % 32.93/33.14 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb0 ]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((op1 (e13) (e13)) = (op1 (e11) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hb2. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hb3. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hb4. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 32.93/33.14 cut (((e11) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb0 ]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e11) = (op1 (e11) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hb6. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hb3. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_Hb7 zenon_Had). % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L33_ *) % 32.93/33.14 assert (zenon_L34_ : ((op1 (e12) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hb8 zenon_H90 zenon_Had zenon_Hb9. % 32.93/33.14 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_Hba | zenon_intro zenon_Hbb ]. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((op1 (e11) (e10)) = (op1 (e12) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hb9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hba. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbc]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e10)) = (op1 (e11) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hbc. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 32.93/33.14 cut (((e11) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbd]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_Hba | zenon_intro zenon_Hbb ]. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((e11) = (op1 (e12) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hbd. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hba. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 32.93/33.14 cut (((op1 (e12) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hbe]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_Hbe zenon_Hb8). % 32.93/33.14 apply zenon_Hbb. apply refl_equal. % 32.93/33.14 apply zenon_Hbb. apply refl_equal. % 32.93/33.14 apply (zenon_L33_); trivial. % 32.93/33.14 apply zenon_Hbb. apply refl_equal. % 32.93/33.14 apply zenon_Hbb. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L34_ *) % 32.93/33.14 assert (zenon_L35_ : (~((op1 (e13) (e13)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e11)) = (e11)) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hbf zenon_Had zenon_H90 zenon_Hc0. % 32.93/33.14 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e13) (e13)) = (op1 (e12) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hbf. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Had. % 32.93/33.14 cut (((e11) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hc1]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb4]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e13) (e13)) = (op1 (e13) (e13)))); [ zenon_intro zenon_Hc2 | zenon_intro zenon_Hb5 ]. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13))) = ((op1 (e11) (e10)) = (op1 (e13) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hb4. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hc2. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb2]. % 32.93/33.14 congruence. % 32.93/33.14 apply (zenon_L33_); trivial. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 apply zenon_Hc1. apply sym_equal. exact zenon_Hc0. % 32.93/33.14 (* end of lemma zenon_L35_ *) % 32.93/33.14 assert (zenon_L36_ : (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e10) (e11)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> ((op1 (e11) (e10)) = (e11)) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hc3 zenon_Hc4 zenon_Hc0 zenon_Had zenon_H90. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e10) (e11)) = (op1 (e12) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hc3. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hbf]. % 32.93/33.14 cut (((e11) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hc5]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e10) (e11)) = (op1 (e10) (e11)))); [ zenon_intro zenon_H96 | zenon_intro zenon_H97 ]. % 32.93/33.14 cut (((op1 (e10) (e11)) = (op1 (e10) (e11))) = ((e11) = (op1 (e10) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hc5. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H96. % 32.93/33.14 cut (((op1 (e10) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H97]. % 32.93/33.14 cut (((op1 (e10) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hc6]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_Hc6 zenon_Hc4). % 32.93/33.14 apply zenon_H97. apply refl_equal. % 32.93/33.14 apply zenon_H97. apply refl_equal. % 32.93/33.14 apply (zenon_L35_); trivial. % 32.93/33.14 (* end of lemma zenon_L36_ *) % 32.93/33.14 assert (zenon_L37_ : (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e12) (e13)) = (e11)) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hc7 zenon_H90 zenon_Hc8. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e12) (e13)) = (op1 (e13) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hc7. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 32.93/33.14 cut (((e11) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hc9]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 32.93/33.14 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e11) = (op1 (e12) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hc9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hca. % 32.93/33.14 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 32.93/33.14 cut (((op1 (e12) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hcc]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_Hcc zenon_Hc8). % 32.93/33.14 apply zenon_Hcb. apply refl_equal. % 32.93/33.14 apply zenon_Hcb. apply refl_equal. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L37_ *) % 32.93/33.14 assert (zenon_L38_ : (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hcd zenon_Hb9 zenon_Had zenon_Hc4 zenon_Hc3 zenon_Hce zenon_Hc7 zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hcf ]. % 32.93/33.14 apply (zenon_L34_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hd0 ]. % 32.93/33.14 apply (zenon_L36_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hc8 ]. % 32.93/33.14 exact (zenon_Hce zenon_Hd1). % 32.93/33.14 apply (zenon_L37_); trivial. % 32.93/33.14 (* end of lemma zenon_L38_ *) % 32.93/33.14 assert (zenon_L39_ : (~((e12) = (e12))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hd2. % 32.93/33.14 apply zenon_Hd2. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L39_ *) % 32.93/33.14 assert (zenon_L40_ : (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e11)) = (e11)) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hd3 zenon_H90 zenon_Hd4. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e11)) = (op1 (e13) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hd3. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 32.93/33.14 cut (((e11) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hd5]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 32.93/33.14 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e11) = (op1 (e13) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hd5. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Ha2. % 32.93/33.14 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 32.93/33.14 cut (((op1 (e13) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hd6]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_Hd6 zenon_Hd4). % 32.93/33.14 apply zenon_Ha3. apply refl_equal. % 32.93/33.14 apply zenon_Ha3. apply refl_equal. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L40_ *) % 32.93/33.14 assert (zenon_L41_ : (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e10) (e13)) = (e11)) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hd7 zenon_H90 zenon_Hd8. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e10) (e13)) = (op1 (e13) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hd7. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 32.93/33.14 cut (((e11) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hd9]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e10) (e13)) = (op1 (e10) (e13)))); [ zenon_intro zenon_Hda | zenon_intro zenon_Hdb ]. % 32.93/33.14 cut (((op1 (e10) (e13)) = (op1 (e10) (e13))) = ((e11) = (op1 (e10) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hd9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hda. % 32.93/33.14 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 32.93/33.14 cut (((op1 (e10) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hdc]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_Hdc zenon_Hd8). % 32.93/33.14 apply zenon_Hdb. apply refl_equal. % 32.93/33.14 apply zenon_Hdb. apply refl_equal. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L41_ *) % 32.93/33.14 assert (zenon_L42_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hdd zenon_Hde zenon_Hdf. % 32.93/33.14 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e12) (e11)) = (op1 (e12) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hdf. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_He0. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_He2]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e12) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_He2. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hdd. % 32.93/33.14 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_He1. apply refl_equal. % 32.93/33.14 apply zenon_He3. apply sym_equal. exact zenon_Hde. % 32.93/33.14 apply zenon_He1. apply refl_equal. % 32.93/33.14 apply zenon_He1. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L42_ *) % 32.93/33.14 assert (zenon_L43_ : ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> False). % 32.93/33.14 do 0 intro. intros zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_He5 zenon_Hac zenon_He6 zenon_Hd7 zenon_He7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_Hdd zenon_He9 zenon_Hb1. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.14 apply (zenon_L30_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Heb | zenon_intro zenon_Hae ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 32.93/33.14 exact (zenon_Hea zenon_Hed). % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 32.93/33.14 apply (zenon_L38_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hf0 ]. % 32.93/33.14 apply (zenon_L38_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_Hae | zenon_intro zenon_Hf1 ]. % 32.93/33.14 exact (zenon_Heb zenon_Hae). % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hd4 ]. % 32.93/33.14 cut (((op1 (e12) (e11)) = (e11)) = ((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_He7. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hc0. % 32.93/33.14 cut (((e11) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_Hf2]. % 32.93/33.14 cut (((op1 (e12) (e11)) = (op1 (e12) (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hf3]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e12) (op1 (e10) (e12))) = (op1 (e12) (op1 (e10) (e12))))); [ zenon_intro zenon_Hf4 | zenon_intro zenon_Hf5 ]. % 32.93/33.14 cut (((op1 (e12) (op1 (e10) (e12))) = (op1 (e12) (op1 (e10) (e12)))) = ((op1 (e12) (e11)) = (op1 (e12) (op1 (e10) (e12))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hf3. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hf4. % 32.93/33.14 cut (((op1 (e12) (op1 (e10) (e12))) = (op1 (e12) (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_Hf5]. % 32.93/33.14 cut (((op1 (e12) (op1 (e10) (e12))) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Hf6]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 32.93/33.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hd2. apply refl_equal. % 32.93/33.14 exact (zenon_Hf7 zenon_Hef). % 32.93/33.14 apply zenon_Hf5. apply refl_equal. % 32.93/33.14 apply zenon_Hf5. apply refl_equal. % 32.93/33.14 apply zenon_Hf2. apply sym_equal. exact zenon_Hef. % 32.93/33.14 apply (zenon_L40_); trivial. % 32.93/33.14 apply (zenon_L41_); trivial. % 32.93/33.14 apply (zenon_L42_); trivial. % 32.93/33.14 apply (zenon_L31_); trivial. % 32.93/33.14 apply (zenon_L27_); trivial. % 32.93/33.14 (* end of lemma zenon_L43_ *) % 32.93/33.14 assert (zenon_L44_ : (~((e11) = (e11))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hf8. % 32.93/33.14 apply zenon_Hf8. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L44_ *) % 32.93/33.14 assert (zenon_L45_ : (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e13)) = (e13)) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hf9 zenon_H90 zenon_Hfa. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((e11) = (e13))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hf9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 32.93/33.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hf8. apply refl_equal. % 32.93/33.14 exact (zenon_Hfb zenon_Hfa). % 32.93/33.14 (* end of lemma zenon_L45_ *) % 32.93/33.14 assert (zenon_L46_ : ((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13))))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hfc zenon_Hfd zenon_Hb1 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_Hac zenon_He5 zenon_H92 zenon_H93 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_Hf9 zenon_H90. % 32.93/33.14 apply (zenon_and_s _ _ zenon_Hfc). zenon_intro zenon_Hff. zenon_intro zenon_Hfe. % 32.93/33.14 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_H101. zenon_intro zenon_H100. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H100). zenon_intro zenon_He7. zenon_intro zenon_H102. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 32.93/33.14 cut (((op1 (e10) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 32.93/33.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_H8e. apply refl_equal. % 32.93/33.14 exact (zenon_H105 zenon_H104). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 32.93/33.14 apply (zenon_L32_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 32.93/33.14 apply (zenon_L43_); trivial. % 32.93/33.14 apply (zenon_L45_); trivial. % 32.93/33.14 (* end of lemma zenon_L46_ *) % 32.93/33.14 assert (zenon_L47_ : (~((h4 (e10)) = (e20))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H107 zenon_H108 zenon_H1a. % 32.93/33.14 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (e10)) = (e20))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H107. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H108. % 32.93/33.14 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 32.93/33.14 cut (((h4 (e10)) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H10a]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_H10a. apply refl_equal. % 32.93/33.14 apply zenon_H109. apply sym_equal. exact zenon_H1a. % 32.93/33.14 (* end of lemma zenon_L47_ *) % 32.93/33.14 assert (zenon_L48_ : (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> ((op1 (e10) (e10)) = (e10)) -> ((op2 (e20) (e20)) = (e20)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H10b zenon_H104 zenon_H14 zenon_H108 zenon_H1a. % 32.93/33.14 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H10b. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H108. % 32.93/33.14 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H10c]. % 32.93/33.14 cut (((h4 (e10)) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H10d]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [ zenon_intro zenon_H10e | zenon_intro zenon_H10f ]. % 32.93/33.14 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10)))) = ((h4 (e10)) = (h4 (op1 (e10) (e10))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H10d. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H10e. % 32.93/33.14 cut (((h4 (op1 (e10) (e10))) = (h4 (op1 (e10) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H10f]. % 32.93/33.14 cut (((h4 (op1 (e10) (e10))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H110]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e10) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H105]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H105 zenon_H104). % 32.93/33.14 apply zenon_H10f. apply refl_equal. % 32.93/33.14 apply zenon_H10f. apply refl_equal. % 32.93/33.14 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H111 | zenon_intro zenon_H112 ]. % 32.93/33.14 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e10)) (h4 (e10))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H10c. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H111. % 32.93/33.14 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 32.93/33.14 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H113]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (h4 (e10)) (h4 (e10))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H113. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H14. % 32.93/33.14 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 32.93/33.14 cut (((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H115]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [ zenon_intro zenon_H111 | zenon_intro zenon_H112 ]. % 32.93/33.14 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10)))) = ((op2 (e20) (e20)) = (op2 (h4 (e10)) (h4 (e10))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H115. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H111. % 32.93/33.14 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (h4 (e10)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H112]. % 32.93/33.14 cut (((op2 (h4 (e10)) (h4 (e10))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H116]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 32.93/33.14 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 32.93/33.14 congruence. % 32.93/33.14 apply (zenon_L47_); trivial. % 32.93/33.14 apply (zenon_L47_); trivial. % 32.93/33.14 apply zenon_H112. apply refl_equal. % 32.93/33.14 apply zenon_H112. apply refl_equal. % 32.93/33.14 exact (zenon_H114 zenon_H1a). % 32.93/33.14 apply zenon_H112. apply refl_equal. % 32.93/33.14 apply zenon_H112. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L48_ *) % 32.93/33.14 assert (zenon_L49_ : (~((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e13) (e12)))) -> ((op1 (e11) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e12)) = (e10)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H117 zenon_Hab zenon_H90 zenon_H118. % 32.93/33.14 cut (((op1 (e11) (e11)) = (e10)) = ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H117. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hab. % 32.93/33.14 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 32.93/33.14 cut (((op1 (e11) (e11)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H11a]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [ zenon_intro zenon_H11b | zenon_intro zenon_H11c ]. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e11) (e11)) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H11a. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H11b. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H11c]. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 32.93/33.14 congruence. % 32.93/33.14 apply (zenon_L26_); trivial. % 32.93/33.14 apply zenon_H11c. apply refl_equal. % 32.93/33.14 apply zenon_H11c. apply refl_equal. % 32.93/33.14 apply zenon_H119. apply sym_equal. exact zenon_H118. % 32.93/33.14 (* end of lemma zenon_L49_ *) % 32.93/33.14 assert (zenon_L50_ : (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e13) (e12)) = (e11)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H11d zenon_H90 zenon_H11e. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e13) (e12)) = (op1 (e13) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H11d. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 32.93/33.14 cut (((e11) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H11f]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H120 | zenon_intro zenon_H121 ]. % 32.93/33.14 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e11) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H11f. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H120. % 32.93/33.14 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 32.93/33.14 cut (((op1 (e13) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H122]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H122 zenon_H11e). % 32.93/33.14 apply zenon_H121. apply refl_equal. % 32.93/33.14 apply zenon_H121. apply refl_equal. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L50_ *) % 32.93/33.14 assert (zenon_L51_ : (~((e13) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H123. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L51_ *) % 32.93/33.14 assert (zenon_L52_ : (~((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H124 zenon_H93. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H125]. % 32.93/33.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 apply zenon_H125. apply sym_equal. exact zenon_H93. % 32.93/33.14 (* end of lemma zenon_L52_ *) % 32.93/33.14 assert (zenon_L53_ : ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e13) (e12)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H126 zenon_H127 zenon_H93 zenon_H128. % 32.93/33.14 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H120 | zenon_intro zenon_H121 ]. % 32.93/33.14 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H128. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H120. % 32.93/33.14 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 32.93/33.14 cut (((op1 (e13) (e12)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H129]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e13) (e12)) = (op1 (e13) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H129. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H126. % 32.93/33.14 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 32.93/33.14 cut (((e12) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12a]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e13) (e12)) = (op1 (e13) (e12)))); [ zenon_intro zenon_H120 | zenon_intro zenon_H121 ]. % 32.93/33.14 cut (((op1 (e13) (e12)) = (op1 (e13) (e12))) = ((e12) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H12a. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H120. % 32.93/33.14 cut (((op1 (e13) (e12)) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H121]. % 32.93/33.14 cut (((op1 (e13) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H12b]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H12b zenon_H127). % 32.93/33.14 apply zenon_H121. apply refl_equal. % 32.93/33.14 apply zenon_H121. apply refl_equal. % 32.93/33.14 apply (zenon_L52_); trivial. % 32.93/33.14 apply zenon_H121. apply refl_equal. % 32.93/33.14 apply zenon_H121. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L53_ *) % 32.93/33.14 assert (zenon_L54_ : (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> ((op1 (e13) (e12)) = (e13)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H12c zenon_H12d zenon_H12e. % 32.93/33.14 cut (((op1 (e13) (e11)) = (e13)) = ((op1 (e13) (e11)) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H12c. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H12d. % 32.93/33.14 cut (((e13) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H12f]. % 32.93/33.14 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Ha3. apply refl_equal. % 32.93/33.14 apply zenon_H12f. apply sym_equal. exact zenon_H12e. % 32.93/33.14 (* end of lemma zenon_L54_ *) % 32.93/33.14 assert (zenon_L55_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((op1 (e11) (e11)) = (e10)) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H130 zenon_Hab zenon_H131 zenon_H132 zenon_H90 zenon_H11d zenon_H128 zenon_H93 zenon_H126 zenon_H12c zenon_H12d. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H118 | zenon_intro zenon_H133 ]. % 32.93/33.14 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e10) (e12)) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H132. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H93. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 32.93/33.14 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e10) (e12)) = (op1 (e10) (e12)))); [ zenon_intro zenon_H135 | zenon_intro zenon_H136 ]. % 32.93/33.14 cut (((op1 (e10) (e12)) = (op1 (e10) (e12))) = ((e10) = (op1 (e10) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H134. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H135. % 32.93/33.14 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 32.93/33.14 cut (((op1 (e10) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H137]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H137 zenon_H131). % 32.93/33.14 apply zenon_H136. apply refl_equal. % 32.93/33.14 apply zenon_H136. apply refl_equal. % 32.93/33.14 apply (zenon_L49_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H11e | zenon_intro zenon_H138 ]. % 32.93/33.14 apply (zenon_L50_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H127 | zenon_intro zenon_H12e ]. % 32.93/33.14 apply (zenon_L53_); trivial. % 32.93/33.14 apply (zenon_L54_); trivial. % 32.93/33.14 (* end of lemma zenon_L55_ *) % 32.93/33.14 assert (zenon_L56_ : (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e10) (e12)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e11)) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H139 zenon_H12d zenon_H12c zenon_H126 zenon_H93 zenon_H128 zenon_H11d zenon_H90 zenon_H132 zenon_H131 zenon_H130 zenon_Heb zenon_H13a zenon_H13b. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H139); [ zenon_intro zenon_Hab | zenon_intro zenon_H13c ]. % 32.93/33.14 apply (zenon_L55_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H13c); [ zenon_intro zenon_Hae | zenon_intro zenon_H13d ]. % 32.93/33.14 exact (zenon_Heb zenon_Hae). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H13d); [ zenon_intro zenon_H13f | zenon_intro zenon_H13e ]. % 32.93/33.14 exact (zenon_H13a zenon_H13f). % 32.93/33.14 exact (zenon_H13b zenon_H13e). % 32.93/33.14 (* end of lemma zenon_L56_ *) % 32.93/33.14 assert (zenon_L57_ : (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e11) (e10)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H140 zenon_H126 zenon_H141 zenon_H93. % 32.93/33.14 cut (((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e11) (e10)) = (op1 (e13) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H140. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H126. % 32.93/33.14 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 32.93/33.14 cut (((e12) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H142]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb0 ]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e12) = (op1 (e11) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H142. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hb3. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H143]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H143 zenon_H141). % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply (zenon_L52_); trivial. % 32.93/33.14 (* end of lemma zenon_L57_ *) % 32.93/33.14 assert (zenon_L58_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e11) (e12)) = (e12)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hdd zenon_H144 zenon_H145. % 32.93/33.14 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e11) (e12)) = (op1 (e12) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H145. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_He0. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H146]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e11) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H146. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hdd. % 32.93/33.14 cut (((e12) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H147]. % 32.93/33.14 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_He1. apply refl_equal. % 32.93/33.14 apply zenon_H147. apply sym_equal. exact zenon_H144. % 32.93/33.14 apply zenon_He1. apply refl_equal. % 32.93/33.14 apply zenon_He1. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L58_ *) % 32.93/33.14 assert (zenon_L59_ : ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e10)) = (e13)) -> (~((e11) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Had zenon_H148 zenon_Hf9. % 32.93/33.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H149 | zenon_intro zenon_H123 ]. % 32.93/33.14 cut (((e13) = (e13)) = ((e11) = (e13))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hf9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H149. % 32.93/33.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 32.93/33.14 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e11) (e10)) = (e11)) = ((e13) = (e11))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H14a. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Had. % 32.93/33.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H14b]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H14b zenon_H148). % 32.93/33.14 apply zenon_Hf8. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L59_ *) % 32.93/33.14 assert (zenon_L60_ : ((op1 (e10) (e13)) = (e10)) -> ((op1 (e10) (e13)) = (e13)) -> (~((e10) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H14c zenon_H14d zenon_H14e. % 32.93/33.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H149 | zenon_intro zenon_H123 ]. % 32.93/33.14 cut (((e13) = (e13)) = ((e10) = (e13))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H14e. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H149. % 32.93/33.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 32.93/33.14 cut (((e13) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H14f]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e10) (e13)) = (e10)) = ((e13) = (e10))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H14f. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H14c. % 32.93/33.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 32.93/33.14 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H150 zenon_H14d). % 32.93/33.14 apply zenon_H8e. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L60_ *) % 32.93/33.14 assert (zenon_L61_ : ((op1 (e11) (e13)) = (e12)) -> ((op1 (e11) (e13)) = (e13)) -> (~((e12) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H151 zenon_H152 zenon_H153. % 32.93/33.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H149 | zenon_intro zenon_H123 ]. % 32.93/33.14 cut (((e13) = (e13)) = ((e12) = (e13))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H153. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H149. % 32.93/33.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 32.93/33.14 cut (((e13) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H154]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e11) (e13)) = (e12)) = ((e13) = (e12))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H154. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H151. % 32.93/33.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 32.93/33.14 cut (((op1 (e11) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H155]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H155 zenon_H152). % 32.93/33.14 apply zenon_Hd2. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L61_ *) % 32.93/33.14 assert (zenon_L62_ : (~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12)))) -> ((op1 (e12) (e13)) = (e13)) -> ((op1 (e11) (e12)) = (e13)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H156 zenon_H157 zenon_H158. % 32.93/33.14 cut (((op1 (e12) (e13)) = (e13)) = ((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H156. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H157. % 32.93/33.14 cut (((e13) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H159]. % 32.93/33.14 cut (((op1 (e12) (e13)) = (op1 (e12) (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H15a]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e12) (op1 (e11) (e12))) = (op1 (e12) (op1 (e11) (e12))))); [ zenon_intro zenon_H15b | zenon_intro zenon_H15c ]. % 32.93/33.14 cut (((op1 (e12) (op1 (e11) (e12))) = (op1 (e12) (op1 (e11) (e12)))) = ((op1 (e12) (e13)) = (op1 (e12) (op1 (e11) (e12))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H15a. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H15b. % 32.93/33.14 cut (((op1 (e12) (op1 (e11) (e12))) = (op1 (e12) (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H15c]. % 32.93/33.14 cut (((op1 (e12) (op1 (e11) (e12))) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H15d]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e11) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 32.93/33.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hd2. apply refl_equal. % 32.93/33.14 exact (zenon_H15e zenon_H158). % 32.93/33.14 apply zenon_H15c. apply refl_equal. % 32.93/33.14 apply zenon_H15c. apply refl_equal. % 32.93/33.14 apply zenon_H159. apply sym_equal. exact zenon_H158. % 32.93/33.14 (* end of lemma zenon_L62_ *) % 32.93/33.14 assert (zenon_L63_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (e13))) -> (~((op1 (e13) (e13)) = (e13))) -> (~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12)))) -> ((op1 (e10) (e13)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H15f zenon_H93 zenon_H126 zenon_H140 zenon_H13a zenon_H145 zenon_Hdd zenon_H160 zenon_Hf9 zenon_Had zenon_H13b zenon_Hfb zenon_H156 zenon_H14c zenon_H14e zenon_H161 zenon_H153. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H141 | zenon_intro zenon_H162 ]. % 32.93/33.14 apply (zenon_L57_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H13f | zenon_intro zenon_H163 ]. % 32.93/33.14 exact (zenon_H13a zenon_H13f). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H144 | zenon_intro zenon_H151 ]. % 32.93/33.14 apply (zenon_L58_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H148 | zenon_intro zenon_H164 ]. % 32.93/33.14 apply (zenon_L59_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H13e | zenon_intro zenon_H165 ]. % 32.93/33.14 exact (zenon_H13b zenon_H13e). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H158 | zenon_intro zenon_H152 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H161); [ zenon_intro zenon_H14d | zenon_intro zenon_H166 ]. % 32.93/33.14 apply (zenon_L60_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H166); [ zenon_intro zenon_H152 | zenon_intro zenon_H167 ]. % 32.93/33.14 apply (zenon_L61_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H167); [ zenon_intro zenon_H157 | zenon_intro zenon_Hfa ]. % 32.93/33.14 apply (zenon_L62_); trivial. % 32.93/33.14 exact (zenon_Hfb zenon_Hfa). % 32.93/33.14 apply (zenon_L61_); trivial. % 32.93/33.14 (* end of lemma zenon_L63_ *) % 32.93/33.14 assert (zenon_L64_ : (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e13)) = (e11)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H168 zenon_H90 zenon_H169. % 32.93/33.14 cut (((e11) = (op1 (e13) (e13))) = ((op1 (e11) (e13)) = (op1 (e13) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H168. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H90. % 32.93/33.14 cut (((op1 (e13) (e13)) = (op1 (e13) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hb5]. % 32.93/33.14 cut (((e11) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16a]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H16b | zenon_intro zenon_H16c ]. % 32.93/33.14 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e11) = (op1 (e11) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H16a. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H16b. % 32.93/33.14 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 32.93/33.14 cut (((op1 (e11) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H16d]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H16d zenon_H169). % 32.93/33.14 apply zenon_H16c. apply refl_equal. % 32.93/33.14 apply zenon_H16c. apply refl_equal. % 32.93/33.14 apply zenon_Hb5. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L64_ *) % 32.93/33.14 assert (zenon_L65_ : (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e11) (e12)) = (e11)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H16e zenon_Had zenon_H16f. % 32.93/33.14 cut (((op1 (e11) (e10)) = (e11)) = ((op1 (e11) (e10)) = (op1 (e11) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H16e. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Had. % 32.93/33.14 cut (((e11) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H170]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply zenon_H170. apply sym_equal. exact zenon_H16f. % 32.93/33.14 (* end of lemma zenon_L65_ *) % 32.93/33.14 assert (zenon_L66_ : ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12)))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H171 zenon_H16e zenon_H172 zenon_H173 zenon_H140 zenon_H145 zenon_Hdd zenon_H160 zenon_H14e zenon_H153 zenon_H156 zenon_H161 zenon_Hf9 zenon_H15f zenon_H130 zenon_H12c zenon_H126 zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H105 zenon_H174 zenon_H168 zenon_H175 zenon_Hb1 zenon_Hac zenon_He5 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.14 apply (zenon_L30_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Heb | zenon_intro zenon_Hae ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H13b | zenon_intro zenon_H169 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.14 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H173); [ zenon_intro zenon_H104 | zenon_intro zenon_H176 ]. % 32.93/33.14 exact (zenon_H105 zenon_H104). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H176); [ zenon_intro zenon_H94 | zenon_intro zenon_H177 ]. % 32.93/33.14 apply (zenon_L27_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H177); [ zenon_intro zenon_H131 | zenon_intro zenon_H14c ]. % 32.93/33.14 apply (zenon_L56_); trivial. % 32.93/33.14 apply (zenon_L63_); trivial. % 32.93/33.14 apply (zenon_L45_); trivial. % 32.93/33.14 apply (zenon_L64_); trivial. % 32.93/33.14 apply (zenon_L65_); trivial. % 32.93/33.14 apply (zenon_L32_); trivial. % 32.93/33.14 (* end of lemma zenon_L66_ *) % 32.93/33.14 assert (zenon_L67_ : ((op1 (e13) (e11)) = (e13)) -> ((op1 (e10) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H12d zenon_H178 zenon_H179. % 32.93/33.14 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 32.93/33.14 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e10) (e11)) = (op1 (e13) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H179. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Ha2. % 32.93/33.14 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 32.93/33.14 cut (((op1 (e13) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H17a]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e13) (e11)) = (e13)) = ((op1 (e13) (e11)) = (op1 (e10) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H17a. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H12d. % 32.93/33.14 cut (((e13) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H17b]. % 32.93/33.14 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Ha3. apply refl_equal. % 32.93/33.14 apply zenon_H17b. apply sym_equal. exact zenon_H178. % 32.93/33.14 apply zenon_Ha3. apply refl_equal. % 32.93/33.14 apply zenon_Ha3. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L67_ *) % 32.93/33.14 assert (zenon_L68_ : ((op1 (e10) (e12)) = (e11)) -> ((op1 (e10) (e12)) = (e13)) -> (~((e11) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Hef zenon_H17c zenon_Hf9. % 32.93/33.14 elim (classic ((e13) = (e13))); [ zenon_intro zenon_H149 | zenon_intro zenon_H123 ]. % 32.93/33.14 cut (((e13) = (e13)) = ((e11) = (e13))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hf9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H149. % 32.93/33.14 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 32.93/33.14 cut (((e13) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H14a]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e10) (e12)) = (e11)) = ((e13) = (e11))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H14a. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hef. % 32.93/33.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 32.93/33.14 cut (((op1 (e10) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H17d]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H17d zenon_H17c). % 32.93/33.14 apply zenon_Hf8. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 apply zenon_H123. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L68_ *) % 32.93/33.14 assert (zenon_L69_ : (~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e12) (e10)) = (e13)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H17e zenon_H14d zenon_H17f. % 32.93/33.14 cut (((op1 (e10) (e13)) = (e13)) = ((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H17e. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H14d. % 32.93/33.14 cut (((e13) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H180]. % 32.93/33.14 cut (((op1 (e10) (e13)) = (op1 (e10) (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H181]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e10) (op1 (e12) (e10))) = (op1 (e10) (op1 (e12) (e10))))); [ zenon_intro zenon_H182 | zenon_intro zenon_H183 ]. % 32.93/33.14 cut (((op1 (e10) (op1 (e12) (e10))) = (op1 (e10) (op1 (e12) (e10)))) = ((op1 (e10) (e13)) = (op1 (e10) (op1 (e12) (e10))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H181. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H182. % 32.93/33.14 cut (((op1 (e10) (op1 (e12) (e10))) = (op1 (e10) (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H183]. % 32.93/33.14 cut (((op1 (e10) (op1 (e12) (e10))) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H184]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 32.93/33.14 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_H8e. apply refl_equal. % 32.93/33.14 exact (zenon_H185 zenon_H17f). % 32.93/33.14 apply zenon_H183. apply refl_equal. % 32.93/33.14 apply zenon_H183. apply refl_equal. % 32.93/33.14 apply zenon_H180. apply sym_equal. exact zenon_H17f. % 32.93/33.14 (* end of lemma zenon_L69_ *) % 32.93/33.14 assert (zenon_L70_ : (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e10)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H186 zenon_H187 zenon_H12d. % 32.93/33.14 cut (((op1 (e13) (e10)) = (e13)) = ((op1 (e13) (e10)) = (op1 (e13) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H186. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H187. % 32.93/33.14 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 32.93/33.14 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_H189. apply refl_equal. % 32.93/33.14 apply zenon_H188. apply sym_equal. exact zenon_H12d. % 32.93/33.14 (* end of lemma zenon_L70_ *) % 32.93/33.14 assert (zenon_L71_ : ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> ((op1 (e13) (e10)) = (e13)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H172 zenon_H187 zenon_H186 zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.14 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.14 apply (zenon_L70_); trivial. % 32.93/33.14 (* end of lemma zenon_L71_ *) % 32.93/33.14 assert (zenon_L72_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e10) (e13)) = (e13)) -> (~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H18a zenon_H18b zenon_Hf9 zenon_Had zenon_H14d zenon_H17e zenon_H172 zenon_H186 zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 32.93/33.14 exact (zenon_H18b zenon_H18d). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H148 | zenon_intro zenon_H18e ]. % 32.93/33.14 apply (zenon_L59_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H17f | zenon_intro zenon_H187 ]. % 32.93/33.14 apply (zenon_L69_); trivial. % 32.93/33.14 apply (zenon_L71_); trivial. % 32.93/33.14 (* end of lemma zenon_L72_ *) % 32.93/33.14 assert (zenon_L73_ : (~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11)))) -> ((op1 (e11) (e12)) = (e12)) -> ((op1 (e12) (e11)) = (e12)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H18f zenon_H144 zenon_Hde. % 32.93/33.14 cut (((op1 (e11) (e12)) = (e12)) = ((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H18f. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H144. % 32.93/33.14 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 32.93/33.14 cut (((op1 (e11) (e12)) = (op1 (e11) (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H190]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e11) (op1 (e12) (e11))) = (op1 (e11) (op1 (e12) (e11))))); [ zenon_intro zenon_H191 | zenon_intro zenon_H192 ]. % 32.93/33.14 cut (((op1 (e11) (op1 (e12) (e11))) = (op1 (e11) (op1 (e12) (e11)))) = ((op1 (e11) (e12)) = (op1 (e11) (op1 (e12) (e11))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H190. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H191. % 32.93/33.14 cut (((op1 (e11) (op1 (e12) (e11))) = (op1 (e11) (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H192]. % 32.93/33.14 cut (((op1 (e11) (op1 (e12) (e11))) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H193]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e12) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 32.93/33.14 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hf8. apply refl_equal. % 32.93/33.14 exact (zenon_H194 zenon_Hde). % 32.93/33.14 apply zenon_H192. apply refl_equal. % 32.93/33.14 apply zenon_H192. apply refl_equal. % 32.93/33.14 apply zenon_He3. apply sym_equal. exact zenon_Hde. % 32.93/33.14 (* end of lemma zenon_L73_ *) % 32.93/33.14 assert (zenon_L74_ : (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e13)) = (e10)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H195 zenon_H104 zenon_H14c. % 32.93/33.14 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e10) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H195. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H104. % 32.93/33.14 cut (((e10) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H196]. % 32.93/33.14 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_H197. apply refl_equal. % 32.93/33.14 apply zenon_H196. apply sym_equal. exact zenon_H14c. % 32.93/33.14 (* end of lemma zenon_L74_ *) % 32.93/33.14 assert (zenon_L75_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> ((op1 (e11) (e13)) = (e12)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H198 zenon_H199 zenon_H151. % 32.93/33.14 cut (((op1 (e10) (e13)) = (e12)) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H198. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H199. % 32.93/33.14 cut (((e12) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 32.93/33.14 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hdb. apply refl_equal. % 32.93/33.14 apply zenon_H19a. apply sym_equal. exact zenon_H151. % 32.93/33.14 (* end of lemma zenon_L75_ *) % 32.93/33.14 assert (zenon_L76_ : (~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H19b zenon_Hdd. % 32.93/33.14 cut (((op1 (e12) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 32.93/33.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hd2. apply refl_equal. % 32.93/33.14 exact (zenon_H19c zenon_Hdd). % 32.93/33.14 (* end of lemma zenon_L76_ *) % 32.93/33.14 assert (zenon_L77_ : ((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13))))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H19d zenon_Hfd zenon_H19e zenon_H171 zenon_H16e zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_H19f zenon_H172 zenon_H186 zenon_H18a zenon_H179 zenon_Hd7 zenon_He6 zenon_H15f zenon_H195 zenon_H198 zenon_H1a0 zenon_H126 zenon_H140 zenon_He9 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_Hf9 zenon_H90. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_H17e. zenon_intro zenon_H1a1. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H18f. zenon_intro zenon_H1a2. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H19b. zenon_intro zenon_H1a3. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.14 apply (zenon_L30_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.14 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 32.93/33.14 exact (zenon_Hea zenon_Hed). % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 32.93/33.14 apply (zenon_L38_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H18d | zenon_intro zenon_H1a4 ]. % 32.93/33.14 exact (zenon_H18b zenon_H18d). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H178 | zenon_intro zenon_H1a5 ]. % 32.93/33.14 apply (zenon_L67_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H17c | zenon_intro zenon_H14d ]. % 32.93/33.14 apply (zenon_L68_); trivial. % 32.93/33.14 apply (zenon_L72_); trivial. % 32.93/33.14 apply (zenon_L41_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.14 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 32.93/33.14 exact (zenon_H18b zenon_H18d). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H148 | zenon_intro zenon_H18e ]. % 32.93/33.14 apply (zenon_L59_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H17f | zenon_intro zenon_H187 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H141 | zenon_intro zenon_H162 ]. % 32.93/33.14 apply (zenon_L57_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H13f | zenon_intro zenon_H163 ]. % 32.93/33.14 exact (zenon_H13a zenon_H13f). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H144 | zenon_intro zenon_H151 ]. % 32.93/33.14 apply (zenon_L73_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1a0); [ zenon_intro zenon_H14c | zenon_intro zenon_H1a6 ]. % 32.93/33.14 apply (zenon_L74_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1a6); [ zenon_intro zenon_Hd8 | zenon_intro zenon_H1a7 ]. % 32.93/33.14 apply (zenon_L41_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1a7); [ zenon_intro zenon_H199 | zenon_intro zenon_H14d ]. % 32.93/33.14 apply (zenon_L75_); trivial. % 32.93/33.14 apply (zenon_L69_); trivial. % 32.93/33.14 apply (zenon_L70_); trivial. % 32.93/33.14 apply (zenon_L65_); trivial. % 32.93/33.14 apply (zenon_L74_); trivial. % 32.93/33.14 apply (zenon_L27_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 32.93/33.14 apply (zenon_L32_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 32.93/33.14 apply (zenon_L76_); trivial. % 32.93/33.14 apply (zenon_L45_); trivial. % 32.93/33.14 (* end of lemma zenon_L77_ *) % 32.93/33.14 assert (zenon_L78_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e12)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H93 zenon_H1a8 zenon_H90 zenon_H1a9. % 32.93/33.14 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1ab ]. % 32.93/33.14 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((op1 (e11) (e11)) = (op1 (e11) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1a9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1aa. % 32.93/33.14 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 32.93/33.14 cut (((op1 (e11) (e12)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H1ac]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e11) (e12)) = (op1 (e11) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1ac. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H93. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 32.93/33.14 cut (((e10) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1ad]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e11) (e12)) = (op1 (e11) (e12)))); [ zenon_intro zenon_H1aa | zenon_intro zenon_H1ab ]. % 32.93/33.14 cut (((op1 (e11) (e12)) = (op1 (e11) (e12))) = ((e10) = (op1 (e11) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1ad. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1aa. % 32.93/33.14 cut (((op1 (e11) (e12)) = (op1 (e11) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H1ab]. % 32.93/33.14 cut (((op1 (e11) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1ae]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H1ae zenon_H1a8). % 32.93/33.14 apply zenon_H1ab. apply refl_equal. % 32.93/33.14 apply zenon_H1ab. apply refl_equal. % 32.93/33.14 apply (zenon_L26_); trivial. % 32.93/33.14 apply zenon_H1ab. apply refl_equal. % 32.93/33.14 apply zenon_H1ab. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L78_ *) % 32.93/33.14 assert (zenon_L79_ : (~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e10)) -> ((op1 (e13) (e12)) = (e10)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1af zenon_H1b0 zenon_H118. % 32.93/33.14 cut (((op1 (e12) (e10)) = (e10)) = ((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1af. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1b0. % 32.93/33.14 cut (((e10) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H119]. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e12) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1b1]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e12) (op1 (e13) (e12))) = (op1 (e12) (op1 (e13) (e12))))); [ zenon_intro zenon_H1b2 | zenon_intro zenon_H1b3 ]. % 32.93/33.14 cut (((op1 (e12) (op1 (e13) (e12))) = (op1 (e12) (op1 (e13) (e12)))) = ((op1 (e12) (e10)) = (op1 (e12) (op1 (e13) (e12))))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1b1. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1b2. % 32.93/33.14 cut (((op1 (e12) (op1 (e13) (e12))) = (op1 (e12) (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H1b3]. % 32.93/33.14 cut (((op1 (e12) (op1 (e13) (e12))) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1b4]. % 32.93/33.14 congruence. % 32.93/33.14 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 32.93/33.14 cut (((e12) = (e12))); [idtac | apply NNPP; zenon_intro zenon_Hd2]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_Hd2. apply refl_equal. % 32.93/33.14 exact (zenon_H1b5 zenon_H118). % 32.93/33.14 apply zenon_H1b3. apply refl_equal. % 32.93/33.14 apply zenon_H1b3. apply refl_equal. % 32.93/33.14 apply zenon_H119. apply sym_equal. exact zenon_H118. % 32.93/33.14 (* end of lemma zenon_L79_ *) % 32.93/33.14 assert (zenon_L80_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> ((op1 (e11) (e11)) = (e10)) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (e10))) -> (~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))) -> ((op1 (e12) (e10)) = (e10)) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1b6 zenon_H12d zenon_H12c zenon_H126 zenon_H128 zenon_H11d zenon_H132 zenon_Hab zenon_H130 zenon_H1a9 zenon_H90 zenon_H93 zenon_H1b7 zenon_H1af zenon_H1b0. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H131 | zenon_intro zenon_H1b8 ]. % 32.93/33.14 apply (zenon_L55_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1b9 ]. % 32.93/33.14 apply (zenon_L78_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H1ba | zenon_intro zenon_H118 ]. % 32.93/33.14 exact (zenon_H1b7 zenon_H1ba). % 32.93/33.14 apply (zenon_L79_); trivial. % 32.93/33.14 (* end of lemma zenon_L80_ *) % 32.93/33.14 assert (zenon_L81_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e12) (e10)) = (e10)) -> (~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Ha7 zenon_H92 zenon_H1b0 zenon_H1af zenon_H1b7 zenon_H1a9 zenon_H130 zenon_H132 zenon_H11d zenon_H128 zenon_H126 zenon_H12c zenon_H12d zenon_H1b6 zenon_H9a zenon_H93 zenon_H90 zenon_Ha1. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H94 | zenon_intro zenon_Ha9 ]. % 32.93/33.14 apply (zenon_L27_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 32.93/33.14 apply (zenon_L80_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H99 | zenon_intro zenon_Ha0 ]. % 32.93/33.14 apply (zenon_L28_); trivial. % 32.93/33.14 apply (zenon_L29_); trivial. % 32.93/33.14 (* end of lemma zenon_L81_ *) % 32.93/33.14 assert (zenon_L82_ : (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (e12)) = (e10))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e10)) -> ((op1 (e11) (e11)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1b6 zenon_H12d zenon_H12c zenon_H126 zenon_H11d zenon_H132 zenon_H130 zenon_H1a9 zenon_H1b7 zenon_H128 zenon_H93 zenon_H1bb zenon_Hab zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H131 | zenon_intro zenon_H1b8 ]. % 32.93/33.14 apply (zenon_L55_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1b9 ]. % 32.93/33.14 apply (zenon_L78_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H1ba | zenon_intro zenon_H118 ]. % 32.93/33.14 exact (zenon_H1b7 zenon_H1ba). % 32.93/33.14 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e13) (e10)) = (op1 (e13) (e12)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H128. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H93. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e13) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H117]. % 32.93/33.14 cut (((e10) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1bc]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e13) (e10)) = (op1 (e13) (e10)))); [ zenon_intro zenon_H1bd | zenon_intro zenon_H189 ]. % 32.93/33.14 cut (((op1 (e13) (e10)) = (op1 (e13) (e10))) = ((e10) = (op1 (e13) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1bc. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1bd. % 32.93/33.14 cut (((op1 (e13) (e10)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H189]. % 32.93/33.14 cut (((op1 (e13) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1be]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H1be zenon_H1bb). % 32.93/33.14 apply zenon_H189. apply refl_equal. % 32.93/33.14 apply zenon_H189. apply refl_equal. % 32.93/33.14 apply (zenon_L49_); trivial. % 32.93/33.14 (* end of lemma zenon_L82_ *) % 32.93/33.14 assert (zenon_L83_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((op1 (e13) (e10)) = (e10)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e12) (e12)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_Ha7 zenon_H92 zenon_H1bb zenon_H128 zenon_H1b7 zenon_H1a9 zenon_H130 zenon_H132 zenon_H11d zenon_H126 zenon_H12c zenon_H12d zenon_H1b6 zenon_H9a zenon_H93 zenon_H90 zenon_Ha1. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H94 | zenon_intro zenon_Ha9 ]. % 32.93/33.14 apply (zenon_L27_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 32.93/33.14 apply (zenon_L82_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H99 | zenon_intro zenon_Ha0 ]. % 32.93/33.14 apply (zenon_L28_); trivial. % 32.93/33.14 apply (zenon_L29_); trivial. % 32.93/33.14 (* end of lemma zenon_L83_ *) % 32.93/33.14 assert (zenon_L84_ : (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e12) (e10)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1bf zenon_H126 zenon_H1c0 zenon_H93. % 32.93/33.14 cut (((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e12) (e10)) = (op1 (e13) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1bf. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H126. % 32.93/33.14 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 32.93/33.14 cut (((e12) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1c1]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e12) (e10)) = (op1 (e12) (e10)))); [ zenon_intro zenon_Hba | zenon_intro zenon_Hbb ]. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e12) (e10))) = ((e12) = (op1 (e12) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1c1. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hba. % 32.93/33.14 cut (((op1 (e12) (e10)) = (op1 (e12) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hbb]. % 32.93/33.14 cut (((op1 (e12) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H1c2]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H1c2 zenon_H1c0). % 32.93/33.14 apply zenon_Hbb. apply refl_equal. % 32.93/33.14 apply zenon_Hbb. apply refl_equal. % 32.93/33.14 apply (zenon_L52_); trivial. % 32.93/33.14 (* end of lemma zenon_L84_ *) % 32.93/33.14 assert (zenon_L85_ : ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1c3 zenon_H1bf zenon_H90 zenon_H1c4 zenon_H92 zenon_H1b6 zenon_H1af zenon_H1a9 zenon_H132 zenon_H11d zenon_H128 zenon_H126 zenon_H12c zenon_H130 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_H93 zenon_Hac zenon_H105 zenon_H172. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1c0 ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.14 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1c4); [ zenon_intro zenon_H104 | zenon_intro zenon_H1c5 ]. % 32.93/33.14 exact (zenon_H105 zenon_H104). % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1c5); [ zenon_intro zenon_H1c7 | zenon_intro zenon_H1c6 ]. % 32.93/33.14 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e11) (e10)) = (op1 (e11) (e11)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_Hac. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H93. % 32.93/33.14 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 32.93/33.14 cut (((e10) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H1c8]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op1 (e11) (e10)) = (op1 (e11) (e10)))); [ zenon_intro zenon_Hb3 | zenon_intro zenon_Hb0 ]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10))) = ((e10) = (op1 (e11) (e10)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1c8. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_Hb3. % 32.93/33.14 cut (((op1 (e11) (e10)) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb0]. % 32.93/33.14 cut (((op1 (e11) (e10)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1c9]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H1c9 zenon_H1c7). % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply zenon_Hb0. apply refl_equal. % 32.93/33.14 apply (zenon_L26_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1c6); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H1bb ]. % 32.93/33.14 apply (zenon_L81_); trivial. % 32.93/33.14 apply (zenon_L83_); trivial. % 32.93/33.14 apply (zenon_L84_); trivial. % 32.93/33.14 (* end of lemma zenon_L85_ *) % 32.93/33.14 assert (zenon_L86_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((op2 (e20) (e20)) = (e20)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1ca zenon_Hd3 zenon_He8 zenon_Hdf zenon_He5 zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_Hf9 zenon_Hb1 zenon_He4 zenon_He9 zenon_H140 zenon_H1a0 zenon_H198 zenon_H195 zenon_H15f zenon_He6 zenon_Hd7 zenon_H179 zenon_H18a zenon_H186 zenon_H19f zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_H16e zenon_H171 zenon_H19e zenon_Hfd zenon_H1cb zenon_H14 zenon_H108 zenon_H1a zenon_H10b zenon_H172 zenon_Hac zenon_H93 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H130 zenon_H12c zenon_H126 zenon_H128 zenon_H11d zenon_H132 zenon_H1a9 zenon_H1b6 zenon_H92 zenon_H1c4 zenon_H90 zenon_H1bf zenon_H1c3. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 32.93/33.14 apply (zenon_L46_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 32.93/33.14 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 32.93/33.14 apply (zenon_L48_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 32.93/33.14 apply (zenon_L32_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 32.93/33.14 apply (zenon_L66_); trivial. % 32.93/33.14 apply (zenon_L48_); trivial. % 32.93/33.14 apply (zenon_L45_); trivial. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 32.93/33.14 apply (zenon_L77_); trivial. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 32.93/33.14 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 32.93/33.14 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 32.93/33.14 apply (zenon_L85_); trivial. % 32.93/33.14 apply (zenon_L48_); trivial. % 32.93/33.14 (* end of lemma zenon_L86_ *) % 32.93/33.14 assert (zenon_L87_ : (~((e23) = (e23))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1da. % 32.93/33.14 apply zenon_H1da. apply refl_equal. % 32.93/33.14 (* end of lemma zenon_L87_ *) % 32.93/33.14 assert (zenon_L88_ : (~((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1db zenon_H1a. % 32.93/33.14 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 32.93/33.14 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 32.93/33.14 congruence. % 32.93/33.14 apply zenon_H1da. apply refl_equal. % 32.93/33.14 apply zenon_H109. apply sym_equal. exact zenon_H1a. % 32.93/33.14 (* end of lemma zenon_L88_ *) % 32.93/33.14 assert (zenon_L89_ : (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e20) (e20)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1dc zenon_H1dd zenon_H1de zenon_H1a. % 32.93/33.14 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e20) (e20)) = (op2 (e23) (e20)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1dc. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1dd. % 32.93/33.14 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 32.93/33.14 cut (((e22) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1df]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op2 (e20) (e20)) = (op2 (e20) (e20)))); [ zenon_intro zenon_H1e0 | zenon_intro zenon_H1e1 ]. % 32.93/33.14 cut (((op2 (e20) (e20)) = (op2 (e20) (e20))) = ((e22) = (op2 (e20) (e20)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1df. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1e0. % 32.93/33.14 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 32.93/33.14 cut (((op2 (e20) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1e2]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H1e2 zenon_H1de). % 32.93/33.14 apply zenon_H1e1. apply refl_equal. % 32.93/33.14 apply zenon_H1e1. apply refl_equal. % 32.93/33.14 apply (zenon_L88_); trivial. % 32.93/33.14 (* end of lemma zenon_L89_ *) % 32.93/33.14 assert (zenon_L90_ : (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e21) (e20)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1e3 zenon_H1dd zenon_H1e4 zenon_H1a. % 32.93/33.14 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e21) (e20)) = (op2 (e23) (e20)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1e3. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1dd. % 32.93/33.14 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 32.93/33.14 cut (((e22) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e5]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op2 (e21) (e20)) = (op2 (e21) (e20)))); [ zenon_intro zenon_H3a | zenon_intro zenon_H37 ]. % 32.93/33.14 cut (((op2 (e21) (e20)) = (op2 (e21) (e20))) = ((e22) = (op2 (e21) (e20)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1e5. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H3a. % 32.93/33.14 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 32.93/33.14 cut (((op2 (e21) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1e6]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H1e6 zenon_H1e4). % 32.93/33.14 apply zenon_H37. apply refl_equal. % 32.93/33.14 apply zenon_H37. apply refl_equal. % 32.93/33.14 apply (zenon_L88_); trivial. % 32.93/33.14 (* end of lemma zenon_L90_ *) % 32.93/33.14 assert (zenon_L91_ : (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e22) (e20)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 32.93/33.14 do 0 intro. intros zenon_H1e7 zenon_H1dd zenon_H1e8 zenon_H1a. % 32.93/33.14 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e22) (e20)) = (op2 (e23) (e20)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1e7. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H1dd. % 32.93/33.14 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 32.93/33.14 cut (((e22) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e9]. % 32.93/33.14 congruence. % 32.93/33.14 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H42 ]. % 32.93/33.14 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e22) = (op2 (e22) (e20)))). % 32.93/33.14 intro zenon_D_pnotp. % 32.93/33.14 apply zenon_H1e9. % 32.93/33.14 rewrite <- zenon_D_pnotp. % 32.93/33.14 exact zenon_H41. % 32.93/33.14 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 32.93/33.14 cut (((op2 (e22) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H1ea]. % 32.93/33.14 congruence. % 32.93/33.14 exact (zenon_H1ea zenon_H1e8). % 32.93/33.15 apply zenon_H42. apply refl_equal. % 32.93/33.15 apply zenon_H42. apply refl_equal. % 32.93/33.15 apply (zenon_L88_); trivial. % 32.93/33.15 (* end of lemma zenon_L91_ *) % 32.93/33.15 assert (zenon_L92_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e21) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H68 zenon_H1eb zenon_H1ec. % 32.93/33.15 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e21) (e22)) = (op2 (e22) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1ec. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H6b. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1ed]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e21) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1ed. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H68. % 32.93/33.15 cut (((e22) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1ee]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H1ee. apply sym_equal. exact zenon_H1eb. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L92_ *) % 32.93/33.15 assert (zenon_L93_ : (~((op2 (e22) (e22)) = (op2 (e20) (e21)))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1ef zenon_H68 zenon_H1f0. % 32.93/33.15 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e20) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1ef. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H68. % 32.93/33.15 cut (((e22) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H1f1. apply sym_equal. exact zenon_H1f0. % 32.93/33.15 (* end of lemma zenon_L93_ *) % 32.93/33.15 assert (zenon_L94_ : (~((op2 (e22) (e22)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1f2 zenon_H1f0 zenon_H68 zenon_H1f3. % 32.93/33.15 cut (((op2 (e20) (e21)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1f2. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1f0. % 32.93/33.15 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 32.93/33.15 cut (((op2 (e20) (e21)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1f5]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e21)) = (op2 (e22) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1f5. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H6b. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1ef]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L93_); trivial. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H1f4. apply sym_equal. exact zenon_H1f3. % 32.93/33.15 (* end of lemma zenon_L94_ *) % 32.93/33.15 assert (zenon_L95_ : (~((op2 (e22) (e22)) = (op2 (e23) (e20)))) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e23) (e20)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1f6 zenon_H68 zenon_H1f0 zenon_H1f3 zenon_H1f7. % 32.93/33.15 cut (((op2 (e21) (e23)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e23) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1f6. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1f3. % 32.93/33.15 cut (((e22) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1f9]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e21) (e23)) = (op2 (e22) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1f9. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H6b. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f2]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L94_); trivial. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H1f8. apply sym_equal. exact zenon_H1f7. % 32.93/33.15 (* end of lemma zenon_L95_ *) % 32.93/33.15 assert (zenon_L96_ : (~((op2 (e22) (e22)) = (e20))) -> ((op2 (e23) (e20)) = (e20)) -> ((op2 (e21) (e23)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e23) (e20)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1fa zenon_H1fb zenon_H1f3 zenon_H1f0 zenon_H68 zenon_H1f7. % 32.93/33.15 cut (((op2 (e23) (e20)) = (e20)) = ((op2 (e22) (e22)) = (e20))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1fa. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1fb. % 32.93/33.15 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 32.93/33.15 cut (((op2 (e23) (e20)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H1fc]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e23) (e20)) = (op2 (e22) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1fc. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H6b. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f6]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L95_); trivial. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H12. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L96_ *) % 32.93/33.15 assert (zenon_L97_ : (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e23) (e22)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1fd zenon_H1fe zenon_H1ff. % 32.93/33.15 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (e20) (e22)) = (op2 (e23) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1fd. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1fe. % 32.93/33.15 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 32.93/33.15 cut (((op2 (e20) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5c]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H5c. apply refl_equal. % 32.93/33.15 apply zenon_H200. apply sym_equal. exact zenon_H1ff. % 32.93/33.15 (* end of lemma zenon_L97_ *) % 32.93/33.15 assert (zenon_L98_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e23)) = (e20))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H201 zenon_H1f7 zenon_H68 zenon_H1f0 zenon_H1f3 zenon_H1fa zenon_H28 zenon_H17 zenon_H1a zenon_H1fe zenon_H1fd zenon_H202. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1fb | zenon_intro zenon_H203 ]. % 32.93/33.15 apply (zenon_L96_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H27 | zenon_intro zenon_H204 ]. % 32.93/33.15 apply (zenon_L6_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H1ff | zenon_intro zenon_H205 ]. % 32.93/33.15 apply (zenon_L97_); trivial. % 32.93/33.15 exact (zenon_H202 zenon_H205). % 32.93/33.15 (* end of lemma zenon_L98_ *) % 32.93/33.15 assert (zenon_L99_ : ((op2 (e22) (e22)) = (e22)) -> ((op2 (e20) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H68 zenon_H206 zenon_H5a. % 32.93/33.15 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H5a. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H6b. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H207. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H68. % 32.93/33.15 cut (((e22) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H208]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H208. apply sym_equal. exact zenon_H206. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L99_ *) % 32.93/33.15 assert (zenon_L100_ : (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H209 zenon_H20a zenon_H1f3. % 32.93/33.15 cut (((op2 (e20) (e23)) = (e22)) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H209. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H20a. % 32.93/33.15 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 apply zenon_H1f4. apply sym_equal. exact zenon_H1f3. % 32.93/33.15 (* end of lemma zenon_L100_ *) % 32.93/33.15 assert (zenon_L101_ : (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H20b zenon_H1a zenon_H1dd zenon_H1e3 zenon_H20c zenon_H1ec zenon_H68 zenon_H209 zenon_H20a. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H20d ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 32.93/33.15 exact (zenon_H20c zenon_H20f). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f3 ]. % 32.93/33.15 apply (zenon_L92_); trivial. % 32.93/33.15 apply (zenon_L100_); trivial. % 32.93/33.15 (* end of lemma zenon_L101_ *) % 32.93/33.15 assert (zenon_L102_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e23) (e23)) = (e20))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((op2 (e20) (e22)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e22)) = (e20))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H210 zenon_H202 zenon_H1fd zenon_H1fe zenon_H17 zenon_H28 zenon_H1fa zenon_H201 zenon_H1e7 zenon_H1dc zenon_H211 zenon_H5a zenon_H20b zenon_H1a zenon_H1dd zenon_H1e3 zenon_H20c zenon_H1ec zenon_H68 zenon_H209. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H1de | zenon_intro zenon_H212 ]. % 32.93/33.15 apply (zenon_L89_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H213 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 32.93/33.15 apply (zenon_L89_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H20d ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 32.93/33.15 exact (zenon_H20c zenon_H20f). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f3 ]. % 32.93/33.15 apply (zenon_L92_); trivial. % 32.93/33.15 apply (zenon_L98_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H206 | zenon_intro zenon_H20a ]. % 32.93/33.15 apply (zenon_L99_); trivial. % 32.93/33.15 apply (zenon_L101_); trivial. % 32.93/33.15 (* end of lemma zenon_L102_ *) % 32.93/33.15 assert (zenon_L103_ : ((op2 (e21) (e20)) = (e21)) -> ((op2 (e21) (e20)) = (e23)) -> (~((e21) = (e23))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H34 zenon_H216 zenon_H83. % 32.93/33.15 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H217 | zenon_intro zenon_H1da ]. % 32.93/33.15 cut (((e23) = (e23)) = ((e21) = (e23))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H83. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H217. % 32.93/33.15 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 32.93/33.15 cut (((e23) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H218]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e21) (e20)) = (e21)) = ((e23) = (e21))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H218. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H34. % 32.93/33.15 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 32.93/33.15 cut (((op2 (e21) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H219]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H219 zenon_H216). % 32.93/33.15 apply zenon_H82. apply refl_equal. % 32.93/33.15 apply zenon_H1da. apply refl_equal. % 32.93/33.15 apply zenon_H1da. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L103_ *) % 32.93/33.15 assert (zenon_L104_ : ((op2 (e20) (e23)) = (e20)) -> ((op2 (e20) (e23)) = (e23)) -> (~((e20) = (e23))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H21a zenon_H21b zenon_H21c. % 32.93/33.15 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H217 | zenon_intro zenon_H1da ]. % 32.93/33.15 cut (((e23) = (e23)) = ((e20) = (e23))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H21c. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H217. % 32.93/33.15 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 32.93/33.15 cut (((e23) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H21d]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e20) (e23)) = (e20)) = ((e23) = (e20))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H21d. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H21a. % 32.93/33.15 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H21e]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H21e zenon_H21b). % 32.93/33.15 apply zenon_H12. apply refl_equal. % 32.93/33.15 apply zenon_H1da. apply refl_equal. % 32.93/33.15 apply zenon_H1da. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L104_ *) % 32.93/33.15 assert (zenon_L105_ : ((op2 (e21) (e23)) = (e22)) -> ((op2 (e21) (e23)) = (e23)) -> (~((e22) = (e23))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1f3 zenon_H21f zenon_H220. % 32.93/33.15 elim (classic ((e23) = (e23))); [ zenon_intro zenon_H217 | zenon_intro zenon_H1da ]. % 32.93/33.15 cut (((e23) = (e23)) = ((e22) = (e23))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H220. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H217. % 32.93/33.15 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 32.93/33.15 cut (((e23) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H221]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e21) (e23)) = (e22)) = ((e23) = (e22))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H221. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1f3. % 32.93/33.15 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H222]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H222 zenon_H21f). % 32.93/33.15 apply zenon_H5d. apply refl_equal. % 32.93/33.15 apply zenon_H1da. apply refl_equal. % 32.93/33.15 apply zenon_H1da. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L105_ *) % 32.93/33.15 assert (zenon_L106_ : (~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22)))) -> ((op2 (e22) (e23)) = (e23)) -> ((op2 (e21) (e22)) = (e23)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H223 zenon_H224 zenon_H225. % 32.93/33.15 cut (((op2 (e22) (e23)) = (e23)) = ((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H223. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H224. % 32.93/33.15 cut (((e23) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H226]. % 32.93/33.15 cut (((op2 (e22) (e23)) = (op2 (e22) (op2 (e21) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H227]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (op2 (e21) (e22))) = (op2 (e22) (op2 (e21) (e22))))); [ zenon_intro zenon_H228 | zenon_intro zenon_H229 ]. % 32.93/33.15 cut (((op2 (e22) (op2 (e21) (e22))) = (op2 (e22) (op2 (e21) (e22)))) = ((op2 (e22) (e23)) = (op2 (e22) (op2 (e21) (e22))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H227. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H228. % 32.93/33.15 cut (((op2 (e22) (op2 (e21) (e22))) = (op2 (e22) (op2 (e21) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H229]. % 32.93/33.15 cut (((op2 (e22) (op2 (e21) (e22))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H22a]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e21) (e22)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H22b]. % 32.93/33.15 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H5d. apply refl_equal. % 32.93/33.15 exact (zenon_H22b zenon_H225). % 32.93/33.15 apply zenon_H229. apply refl_equal. % 32.93/33.15 apply zenon_H229. apply refl_equal. % 32.93/33.15 apply zenon_H226. apply sym_equal. exact zenon_H225. % 32.93/33.15 (* end of lemma zenon_L106_ *) % 32.93/33.15 assert (zenon_L107_ : (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e21) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/((op2 (e21) (e23)) = (e23))))) -> (~((e21) = (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e21)) = (e23))) -> (~((op2 (e23) (e23)) = (e23))) -> (~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22)))) -> ((op2 (e20) (e23)) = (e20)) -> (~((e20) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H20b zenon_H1a zenon_H1dd zenon_H1e3 zenon_H20c zenon_H1ec zenon_H68 zenon_H22c zenon_H83 zenon_H34 zenon_H22d zenon_H85 zenon_H223 zenon_H21a zenon_H21c zenon_H22e zenon_H220. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H20d ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 32.93/33.15 exact (zenon_H20c zenon_H20f). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f3 ]. % 32.93/33.15 apply (zenon_L92_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H22c); [ zenon_intro zenon_H216 | zenon_intro zenon_H22f ]. % 32.93/33.15 apply (zenon_L103_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H22f); [ zenon_intro zenon_H231 | zenon_intro zenon_H230 ]. % 32.93/33.15 exact (zenon_H22d zenon_H231). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H230); [ zenon_intro zenon_H225 | zenon_intro zenon_H21f ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H22e); [ zenon_intro zenon_H21b | zenon_intro zenon_H232 ]. % 32.93/33.15 apply (zenon_L104_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H232); [ zenon_intro zenon_H21f | zenon_intro zenon_H233 ]. % 32.93/33.15 apply (zenon_L105_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H233); [ zenon_intro zenon_H224 | zenon_intro zenon_H84 ]. % 32.93/33.15 apply (zenon_L106_); trivial. % 32.93/33.15 exact (zenon_H85 zenon_H84). % 32.93/33.15 apply (zenon_L105_); trivial. % 32.93/33.15 (* end of lemma zenon_L107_ *) % 32.93/33.15 assert (zenon_L108_ : (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((op2 (e23) (e20)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H234 zenon_H235 zenon_H236. % 32.93/33.15 cut (((op2 (e23) (e20)) = (e23)) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H234. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H235. % 32.93/33.15 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H237]. % 32.93/33.15 cut (((op2 (e23) (e20)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H238]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H238. apply refl_equal. % 32.93/33.15 apply zenon_H237. apply sym_equal. exact zenon_H236. % 32.93/33.15 (* end of lemma zenon_L108_ *) % 32.93/33.15 assert (zenon_L109_ : ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((op2 (e23) (e20)) = (e23)) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H239 zenon_H235 zenon_H234 zenon_H17. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H18 | zenon_intro zenon_H236 ]. % 32.93/33.15 apply zenon_H18. apply sym_equal. exact zenon_H17. % 32.93/33.15 apply (zenon_L108_); trivial. % 32.93/33.15 (* end of lemma zenon_L109_ *) % 32.93/33.15 assert (zenon_L110_ : (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e23)) = (e21)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H23a zenon_H17 zenon_H23b. % 32.93/33.15 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e21) (e23)) = (op2 (e23) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H23a. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H17. % 32.93/33.15 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 32.93/33.15 cut (((e21) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23c]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H23d | zenon_intro zenon_H23e ]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e21) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H23c. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H23d. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H23f]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H23f zenon_H23b). % 32.93/33.15 apply zenon_H23e. apply refl_equal. % 32.93/33.15 apply zenon_H23e. apply refl_equal. % 32.93/33.15 apply zenon_H3c. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L110_ *) % 32.93/33.15 assert (zenon_L111_ : (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e21) (e22)) = (e21)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H240 zenon_H34 zenon_H241. % 32.93/33.15 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (e21) (e20)) = (op2 (e21) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H240. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H34. % 32.93/33.15 cut (((e21) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H242]. % 32.93/33.15 cut (((op2 (e21) (e20)) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H37]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H37. apply refl_equal. % 32.93/33.15 apply zenon_H242. apply sym_equal. exact zenon_H241. % 32.93/33.15 (* end of lemma zenon_L111_ *) % 32.93/33.15 assert (zenon_L112_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (((op2 (e21) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/((op2 (e21) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((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)) = (e20))) -> ((~((op2 (e23) (e23)) = (e23)))\/((op2 (e23) (e23)) = (e23))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H38 zenon_H243 zenon_H23a zenon_H244 zenon_H234 zenon_H239 zenon_H245 zenon_H22c zenon_H21c zenon_H220 zenon_H223 zenon_H22e zenon_H83 zenon_H1dc zenon_H1dd zenon_H211 zenon_H1ec zenon_H68 zenon_H201 zenon_H1fd zenon_H20b zenon_H1e7 zenon_H1e3 zenon_H5a zenon_H209 zenon_H210 zenon_H15 zenon_H246 zenon_H247 zenon_H240 zenon_H248 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 32.93/33.15 apply (zenon_L7_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H243); [ zenon_intro zenon_H22d | zenon_intro zenon_H23b ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H202 | zenon_intro zenon_H235 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H246); [ zenon_intro zenon_H85 | zenon_intro zenon_H84 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H14 | zenon_intro zenon_H249 ]. % 32.93/33.15 exact (zenon_H15 zenon_H14). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1b | zenon_intro zenon_H24a ]. % 32.93/33.15 apply (zenon_L4_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1fe | zenon_intro zenon_H21a ]. % 32.93/33.15 apply (zenon_L102_); trivial. % 32.93/33.15 apply (zenon_L107_); trivial. % 32.93/33.15 apply (zenon_L23_); trivial. % 32.93/33.15 apply (zenon_L109_); trivial. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_L110_); trivial. % 32.93/33.15 apply (zenon_L111_); trivial. % 32.93/33.15 (* end of lemma zenon_L112_ *) % 32.93/33.15 assert (zenon_L113_ : (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e23)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H24b zenon_H14 zenon_H21a. % 32.93/33.15 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (e20) (e20)) = (op2 (e20) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H24b. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H14. % 32.93/33.15 cut (((e20) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 32.93/33.15 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H1e1. apply refl_equal. % 32.93/33.15 apply zenon_H24c. apply sym_equal. exact zenon_H21a. % 32.93/33.15 (* end of lemma zenon_L113_ *) % 32.93/33.15 assert (zenon_L114_ : (~((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e20) (e21)))) -> ((op2 (e23) (e20)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e21)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H24d zenon_H1f7 zenon_H1a zenon_H1f0. % 32.93/33.15 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e20) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H24d. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1f7. % 32.93/33.15 cut (((e22) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H1f1]. % 32.93/33.15 cut (((op2 (e23) (e20)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [ zenon_intro zenon_H24f | zenon_intro zenon_H250 ]. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e23) (e20)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H24e. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H24f. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H250]. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L88_); trivial. % 32.93/33.15 apply zenon_H250. apply refl_equal. % 32.93/33.15 apply zenon_H250. apply refl_equal. % 32.93/33.15 apply zenon_H1f1. apply sym_equal. exact zenon_H1f0. % 32.93/33.15 (* end of lemma zenon_L114_ *) % 32.93/33.15 assert (zenon_L115_ : ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e20) (e23)) = (e22)) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1dd zenon_H20a zenon_H1f7 zenon_H1f0 zenon_H1a zenon_H251. % 32.93/33.15 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((op2 (e20) (e21)) = (op2 (e20) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H251. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H65. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H252]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e20) (e23)) = (op2 (e20) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H252. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1dd. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 32.93/33.15 cut (((e22) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H253]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e22) = (op2 (e20) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H253. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H65. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H254]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H254 zenon_H20a). % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 apply (zenon_L114_); trivial. % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L115_ *) % 32.93/33.15 assert (zenon_L116_ : (~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21)))) -> ((op2 (e21) (e22)) = (e22)) -> ((op2 (e22) (e21)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H255 zenon_H1eb zenon_H69. % 32.93/33.15 cut (((op2 (e21) (e22)) = (e22)) = ((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H255. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1eb. % 32.93/33.15 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 32.93/33.15 cut (((op2 (e21) (e22)) = (op2 (e21) (op2 (e22) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H256]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e21) (op2 (e22) (e21))) = (op2 (e21) (op2 (e22) (e21))))); [ zenon_intro zenon_H257 | zenon_intro zenon_H258 ]. % 32.93/33.15 cut (((op2 (e21) (op2 (e22) (e21))) = (op2 (e21) (op2 (e22) (e21)))) = ((op2 (e21) (e22)) = (op2 (e21) (op2 (e22) (e21))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H256. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H257. % 32.93/33.15 cut (((op2 (e21) (op2 (e22) (e21))) = (op2 (e21) (op2 (e22) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H258]. % 32.93/33.15 cut (((op2 (e21) (op2 (e22) (e21))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H259]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e22) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 32.93/33.15 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H82. apply refl_equal. % 32.93/33.15 exact (zenon_H25a zenon_H69). % 32.93/33.15 apply zenon_H258. apply refl_equal. % 32.93/33.15 apply zenon_H258. apply refl_equal. % 32.93/33.15 apply zenon_H6e. apply sym_equal. exact zenon_H69. % 32.93/33.15 (* end of lemma zenon_L116_ *) % 32.93/33.15 assert (zenon_L117_ : ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e23) (e21)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1dd zenon_H25b zenon_H1a zenon_H234. % 32.93/33.15 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H29 | zenon_intro zenon_H2a ]. % 32.93/33.15 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((op2 (e23) (e20)) = (op2 (e23) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H234. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H29. % 32.93/33.15 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 32.93/33.15 cut (((op2 (e23) (e21)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H25c]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e23) (e21)) = (op2 (e23) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H25c. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1dd. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 32.93/33.15 cut (((e22) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H25d]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e23) (e21)) = (op2 (e23) (e21)))); [ zenon_intro zenon_H29 | zenon_intro zenon_H2a ]. % 32.93/33.15 cut (((op2 (e23) (e21)) = (op2 (e23) (e21))) = ((e22) = (op2 (e23) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H25d. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H29. % 32.93/33.15 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 32.93/33.15 cut (((op2 (e23) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H25e]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H25e zenon_H25b). % 32.93/33.15 apply zenon_H2a. apply refl_equal. % 32.93/33.15 apply zenon_H2a. apply refl_equal. % 32.93/33.15 apply (zenon_L88_); trivial. % 32.93/33.15 apply zenon_H2a. apply refl_equal. % 32.93/33.15 apply zenon_H2a. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L117_ *) % 32.93/33.15 assert (zenon_L118_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H211 zenon_H1e2 zenon_H1e7 zenon_H20b zenon_H1e3 zenon_H234 zenon_H1a zenon_H1dd zenon_H255 zenon_H20c zenon_H251 zenon_H25f zenon_H209 zenon_H20a. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 32.93/33.15 exact (zenon_H1e2 zenon_H1de). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H20d ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 32.93/33.15 exact (zenon_H20c zenon_H20f). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f3 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H260 ]. % 32.93/33.15 apply (zenon_L115_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 32.93/33.15 exact (zenon_H20c zenon_H20f). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H69 | zenon_intro zenon_H25b ]. % 32.93/33.15 apply (zenon_L116_); trivial. % 32.93/33.15 apply (zenon_L117_); trivial. % 32.93/33.15 apply (zenon_L100_); trivial. % 32.93/33.15 (* end of lemma zenon_L118_ *) % 32.93/33.15 assert (zenon_L119_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))) -> ((op2 (e21) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e20) (e20)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H262 zenon_H32 zenon_H17 zenon_H14. % 32.93/33.15 cut (((op2 (e21) (e21)) = (e20)) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H262. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H32. % 32.93/33.15 cut (((e20) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H263]. % 32.93/33.15 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [ zenon_intro zenon_H265 | zenon_intro zenon_H266 ]. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H264. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H265. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L3_); trivial. % 32.93/33.15 apply zenon_H266. apply refl_equal. % 32.93/33.15 apply zenon_H266. apply refl_equal. % 32.93/33.15 apply zenon_H263. apply sym_equal. exact zenon_H14. % 32.93/33.15 (* end of lemma zenon_L119_ *) % 32.93/33.15 assert (zenon_L120_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e20)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> ((op2 (e20) (e20)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1a zenon_H267 zenon_H32 zenon_H14 zenon_H17 zenon_H268. % 32.93/33.15 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H42 ]. % 32.93/33.15 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((op2 (e20) (e20)) = (op2 (e22) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H268. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H41. % 32.93/33.15 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 32.93/33.15 cut (((op2 (e22) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H269]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e22) (e20)) = (op2 (e20) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H269. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1a. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H262]. % 32.93/33.15 cut (((e20) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H26a]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (e20)) = (op2 (e22) (e20)))); [ zenon_intro zenon_H41 | zenon_intro zenon_H42 ]. % 32.93/33.15 cut (((op2 (e22) (e20)) = (op2 (e22) (e20))) = ((e20) = (op2 (e22) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H26a. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H41. % 32.93/33.15 cut (((op2 (e22) (e20)) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H42]. % 32.93/33.15 cut (((op2 (e22) (e20)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H26b]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H26b zenon_H267). % 32.93/33.15 apply zenon_H42. apply refl_equal. % 32.93/33.15 apply zenon_H42. apply refl_equal. % 32.93/33.15 apply (zenon_L119_); trivial. % 32.93/33.15 apply zenon_H42. apply refl_equal. % 32.93/33.15 apply zenon_H42. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L120_ *) % 32.93/33.15 assert (zenon_L121_ : (~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e22) (e20)) = (e23)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H26c zenon_H21b zenon_H26d. % 32.93/33.15 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H26c. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H21b. % 32.93/33.15 cut (((e23) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H26e]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (op2 (e22) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H26f]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e20) (op2 (e22) (e20))) = (op2 (e20) (op2 (e22) (e20))))); [ zenon_intro zenon_H270 | zenon_intro zenon_H271 ]. % 32.93/33.15 cut (((op2 (e20) (op2 (e22) (e20))) = (op2 (e20) (op2 (e22) (e20)))) = ((op2 (e20) (e23)) = (op2 (e20) (op2 (e22) (e20))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H26f. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H270. % 32.93/33.15 cut (((op2 (e20) (op2 (e22) (e20))) = (op2 (e20) (op2 (e22) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H271]. % 32.93/33.15 cut (((op2 (e20) (op2 (e22) (e20))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H272]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e22) (e20)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H273]. % 32.93/33.15 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H12. apply refl_equal. % 32.93/33.15 exact (zenon_H273 zenon_H26d). % 32.93/33.15 apply zenon_H271. apply refl_equal. % 32.93/33.15 apply zenon_H271. apply refl_equal. % 32.93/33.15 apply zenon_H26e. apply sym_equal. exact zenon_H26d. % 32.93/33.15 (* end of lemma zenon_L121_ *) % 32.93/33.15 assert (zenon_L122_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20)))) -> ((op2 (e20) (e23)) = (e23)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H274 zenon_H268 zenon_H14 zenon_H32 zenon_H40 zenon_H34 zenon_H17 zenon_H1a zenon_H1dd zenon_H1e7 zenon_H26c zenon_H21b. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H267 | zenon_intro zenon_H275 ]. % 32.93/33.15 apply (zenon_L120_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H3f | zenon_intro zenon_H276 ]. % 32.93/33.15 apply (zenon_L11_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H26d ]. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_L121_); trivial. % 32.93/33.15 (* end of lemma zenon_L122_ *) % 32.93/33.15 assert (zenon_L123_ : (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2e zenon_H19 zenon_H21b zenon_H26c zenon_H1e7 zenon_H1dd zenon_H34 zenon_H40 zenon_H14 zenon_H268 zenon_H274 zenon_H21 zenon_H1a zenon_H17 zenon_H28. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H1b | zenon_intro zenon_H30 ]. % 32.93/33.15 apply (zenon_L4_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 32.93/33.15 apply (zenon_L122_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H20 | zenon_intro zenon_H27 ]. % 32.93/33.15 apply (zenon_L5_); trivial. % 32.93/33.15 apply (zenon_L6_); trivial. % 32.93/33.15 (* end of lemma zenon_L123_ *) % 32.93/33.15 assert (zenon_L124_ : (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e20) (e22)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H277 zenon_H14 zenon_H1fe. % 32.93/33.15 cut (((op2 (e20) (e20)) = (e20)) = ((op2 (e20) (e20)) = (op2 (e20) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H277. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H14. % 32.93/33.15 cut (((e20) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H278]. % 32.93/33.15 cut (((op2 (e20) (e20)) = (op2 (e20) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1e1]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H1e1. apply refl_equal. % 32.93/33.15 apply zenon_H278. apply sym_equal. exact zenon_H1fe. % 32.93/33.15 (* end of lemma zenon_L124_ *) % 32.93/33.15 assert (zenon_L125_ : ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H279 zenon_H277 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_H24b zenon_H14 zenon_H62 zenon_H211 zenon_H25f zenon_H234 zenon_H255 zenon_H251 zenon_H209 zenon_H20b zenon_H1e7 zenon_H1dd zenon_H1e3 zenon_H268 zenon_H40 zenon_H26c zenon_H274 zenon_H27a zenon_H38. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 32.93/33.15 apply (zenon_L7_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H21a | zenon_intro zenon_H27b ]. % 32.93/33.15 apply (zenon_L113_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H63 | zenon_intro zenon_H27c ]. % 32.93/33.15 apply (zenon_L19_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H20a | zenon_intro zenon_H21b ]. % 32.93/33.15 apply (zenon_L118_); trivial. % 32.93/33.15 apply (zenon_L123_); trivial. % 32.93/33.15 apply (zenon_L111_); trivial. % 32.93/33.15 apply (zenon_L124_); trivial. % 32.93/33.15 (* end of lemma zenon_L125_ *) % 32.93/33.15 assert (zenon_L126_ : (~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H27d zenon_H68. % 32.93/33.15 cut (((op2 (e22) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H27e]. % 32.93/33.15 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H5d. apply refl_equal. % 32.93/33.15 exact (zenon_H27e zenon_H68). % 32.93/33.15 (* end of lemma zenon_L126_ *) % 32.93/33.15 assert (zenon_L127_ : ((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H27f zenon_H87 zenon_H27a zenon_H274 zenon_H40 zenon_H268 zenon_H1e3 zenon_H1dd zenon_H1e7 zenon_H20b zenon_H209 zenon_H251 zenon_H234 zenon_H25f zenon_H211 zenon_H62 zenon_H24b zenon_H240 zenon_H248 zenon_H277 zenon_H279 zenon_H2e zenon_H28 zenon_H21 zenon_H1a zenon_H19 zenon_H33 zenon_H38 zenon_H83 zenon_H17. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H26c. zenon_intro zenon_H280. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_H255. zenon_intro zenon_H281. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H281). zenon_intro zenon_H27d. zenon_intro zenon_H282. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 32.93/33.15 apply (zenon_L125_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 32.93/33.15 apply (zenon_L9_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 32.93/33.15 apply (zenon_L126_); trivial. % 32.93/33.15 apply (zenon_L23_); trivial. % 32.93/33.15 (* end of lemma zenon_L127_ *) % 32.93/33.15 assert (zenon_L128_ : (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (e22)))) -> ((op2 (e23) (e20)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H283 zenon_H1f7. % 32.93/33.15 cut (((op2 (e23) (e20)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H284]. % 32.93/33.15 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H12. apply refl_equal. % 32.93/33.15 exact (zenon_H284 zenon_H1f7). % 32.93/33.15 (* end of lemma zenon_L128_ *) % 32.93/33.15 assert (zenon_L129_ : (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> ((op2 (e20) (e22)) = (e20)) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e23) (e20)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H285 zenon_H1fe zenon_H1f7 zenon_H1fb. % 32.93/33.15 cut (((op2 (e20) (e22)) = (e20)) = ((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H285. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1fe. % 32.93/33.15 cut (((e20) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H286]. % 32.93/33.15 cut (((op2 (e20) (e22)) = (op2 (e20) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (op2 (e23) (e20))))); [ zenon_intro zenon_H288 | zenon_intro zenon_H289 ]. % 32.93/33.15 cut (((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (op2 (e23) (e20)))) = ((op2 (e20) (e22)) = (op2 (e20) (op2 (e23) (e20))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H287. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H288. % 32.93/33.15 cut (((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 32.93/33.15 cut (((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L128_); trivial. % 32.93/33.15 apply zenon_H289. apply refl_equal. % 32.93/33.15 apply zenon_H289. apply refl_equal. % 32.93/33.15 apply zenon_H286. apply sym_equal. exact zenon_H1fb. % 32.93/33.15 (* end of lemma zenon_L129_ *) % 32.93/33.15 assert (zenon_L130_ : (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e23) (e20)) = (e22)) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e23)) = (e20))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H201 zenon_H1f7 zenon_H285 zenon_H28 zenon_H17 zenon_H1a zenon_H1fe zenon_H1fd zenon_H202. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H201); [ zenon_intro zenon_H1fb | zenon_intro zenon_H203 ]. % 32.93/33.15 apply (zenon_L129_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H203); [ zenon_intro zenon_H27 | zenon_intro zenon_H204 ]. % 32.93/33.15 apply (zenon_L6_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H204); [ zenon_intro zenon_H1ff | zenon_intro zenon_H205 ]. % 32.93/33.15 apply (zenon_L97_); trivial. % 32.93/33.15 exact (zenon_H202 zenon_H205). % 32.93/33.15 (* end of lemma zenon_L130_ *) % 32.93/33.15 assert (zenon_L131_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e22)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1a zenon_H28a zenon_H17 zenon_H28b. % 32.93/33.15 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 32.93/33.15 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((op2 (e21) (e21)) = (op2 (e21) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H28b. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H28c. % 32.93/33.15 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 32.93/33.15 cut (((op2 (e21) (e22)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H28e]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e21) (e22)) = (op2 (e21) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H28e. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1a. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 32.93/33.15 cut (((e20) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H28f]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e21) (e22)) = (op2 (e21) (e22)))); [ zenon_intro zenon_H28c | zenon_intro zenon_H28d ]. % 32.93/33.15 cut (((op2 (e21) (e22)) = (op2 (e21) (e22))) = ((e20) = (op2 (e21) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H28f. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H28c. % 32.93/33.15 cut (((op2 (e21) (e22)) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H28d]. % 32.93/33.15 cut (((op2 (e21) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H290]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H290 zenon_H28a). % 32.93/33.15 apply zenon_H28d. apply refl_equal. % 32.93/33.15 apply zenon_H28d. apply refl_equal. % 32.93/33.15 apply (zenon_L3_); trivial. % 32.93/33.15 apply zenon_H28d. apply refl_equal. % 32.93/33.15 apply zenon_H28d. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L131_ *) % 32.93/33.15 assert (zenon_L132_ : (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e22) (e20)))) -> ((op2 (e23) (e22)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H291 zenon_H1ff. % 32.93/33.15 cut (((op2 (e23) (e22)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H292]. % 32.93/33.15 cut (((e22) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H5d]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H5d. apply refl_equal. % 32.93/33.15 exact (zenon_H292 zenon_H1ff). % 32.93/33.15 (* end of lemma zenon_L132_ *) % 32.93/33.15 assert (zenon_L133_ : (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> ((op2 (e22) (e20)) = (e20)) -> ((op2 (e23) (e22)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H293 zenon_H267 zenon_H1ff. % 32.93/33.15 cut (((op2 (e22) (e20)) = (e20)) = ((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H293. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H267. % 32.93/33.15 cut (((e20) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H200]. % 32.93/33.15 cut (((op2 (e22) (e20)) = (op2 (e22) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H294]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (op2 (e23) (e22))) = (op2 (e22) (op2 (e23) (e22))))); [ zenon_intro zenon_H295 | zenon_intro zenon_H296 ]. % 32.93/33.15 cut (((op2 (e22) (op2 (e23) (e22))) = (op2 (e22) (op2 (e23) (e22)))) = ((op2 (e22) (e20)) = (op2 (e22) (op2 (e23) (e22))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H294. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H295. % 32.93/33.15 cut (((op2 (e22) (op2 (e23) (e22))) = (op2 (e22) (op2 (e23) (e22))))); [idtac | apply NNPP; zenon_intro zenon_H296]. % 32.93/33.15 cut (((op2 (e22) (op2 (e23) (e22))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H291]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L132_); trivial. % 32.93/33.15 apply zenon_H296. apply refl_equal. % 32.93/33.15 apply zenon_H296. apply refl_equal. % 32.93/33.15 apply zenon_H200. apply sym_equal. exact zenon_H1ff. % 32.93/33.15 (* end of lemma zenon_L133_ *) % 32.93/33.15 assert (zenon_L134_ : (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e23) (e23)) = (e20))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> ((op2 (e23) (e20)) = (e22)) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> ((op2 (e22) (e20)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H297 zenon_H202 zenon_H1fd zenon_H28 zenon_H285 zenon_H1f7 zenon_H201 zenon_H28b zenon_H17 zenon_H1a zenon_H1fa zenon_H293 zenon_H267. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_H1fe | zenon_intro zenon_H298 ]. % 32.93/33.15 apply (zenon_L130_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H28a | zenon_intro zenon_H299 ]. % 32.93/33.15 apply (zenon_L131_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_H29a | zenon_intro zenon_H1ff ]. % 32.93/33.15 exact (zenon_H1fa zenon_H29a). % 32.93/33.15 apply (zenon_L133_); trivial. % 32.93/33.15 (* end of lemma zenon_L134_ *) % 32.93/33.15 assert (zenon_L135_ : (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e23)))) -> ((op2 (e21) (e21)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e22) (e23)) = (e20)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H29b zenon_H32 zenon_H17 zenon_H29c. % 32.93/33.15 cut (((op2 (e21) (e21)) = (e20)) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H29b. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H32. % 32.93/33.15 cut (((e20) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H29d]. % 32.93/33.15 cut (((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H264]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [ zenon_intro zenon_H265 | zenon_intro zenon_H266 ]. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e21) (e21)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H264. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H265. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H266]. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L3_); trivial. % 32.93/33.15 apply zenon_H266. apply refl_equal. % 32.93/33.15 apply zenon_H266. apply refl_equal. % 32.93/33.15 apply zenon_H29d. apply sym_equal. exact zenon_H29c. % 32.93/33.15 (* end of lemma zenon_L135_ *) % 32.93/33.15 assert (zenon_L136_ : ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> ((op2 (e20) (e23)) = (e20)) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H244 zenon_H234 zenon_H239 zenon_H1e2 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H1e7 zenon_H2e zenon_H297 zenon_H293 zenon_H1fa zenon_H28b zenon_H285 zenon_H28 zenon_H1fd zenon_H201 zenon_H21 zenon_H29e zenon_H21a zenon_H29f zenon_H17 zenon_H19 zenon_H211. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H202 | zenon_intro zenon_H235 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 32.93/33.15 exact (zenon_H1e2 zenon_H1de). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H1b | zenon_intro zenon_H30 ]. % 32.93/33.15 apply (zenon_L4_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H29f); [ zenon_intro zenon_H267 | zenon_intro zenon_H2a0 ]. % 32.93/33.15 apply (zenon_L134_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2a0); [ zenon_intro zenon_H20 | zenon_intro zenon_H2a1 ]. % 32.93/33.15 apply (zenon_L5_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H29a | zenon_intro zenon_H29c ]. % 32.93/33.15 exact (zenon_H1fa zenon_H29a). % 32.93/33.15 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e20) (e23)) = (op2 (e22) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H29e. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1a. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H29b]. % 32.93/33.15 cut (((e20) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H24c]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e20) (e23)) = (op2 (e20) (e23)))); [ zenon_intro zenon_H65 | zenon_intro zenon_H66 ]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23))) = ((e20) = (op2 (e20) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H24c. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H65. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2a2]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H2a2 zenon_H21a). % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 apply (zenon_L135_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H20 | zenon_intro zenon_H27 ]. % 32.93/33.15 apply (zenon_L5_); trivial. % 32.93/33.15 apply (zenon_L6_); trivial. % 32.93/33.15 apply (zenon_L109_); trivial. % 32.93/33.15 (* end of lemma zenon_L136_ *) % 32.93/33.15 assert (zenon_L137_ : ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((op2 (e20) (e22)) = (e20)) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H244 zenon_H234 zenon_H239 zenon_H1dc zenon_H1dd zenon_H1a zenon_H1e3 zenon_H1e7 zenon_H201 zenon_H1fd zenon_H17 zenon_H28 zenon_H1fe zenon_H285 zenon_H211. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H202 | zenon_intro zenon_H235 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 32.93/33.15 apply (zenon_L89_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_L130_); trivial. % 32.93/33.15 apply (zenon_L109_); trivial. % 32.93/33.15 (* end of lemma zenon_L137_ *) % 32.93/33.15 assert (zenon_L138_ : ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e20)) = (e20))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H279 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_H15 zenon_H210 zenon_H209 zenon_H5a zenon_H1e3 zenon_H1e7 zenon_H20b zenon_H1fd zenon_H201 zenon_H68 zenon_H1ec zenon_H211 zenon_H1dd zenon_H1dc zenon_H244 zenon_H234 zenon_H239 zenon_H297 zenon_H293 zenon_H28b zenon_H285 zenon_H29e zenon_H29f zenon_H245 zenon_H247 zenon_H38. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 32.93/33.15 apply (zenon_L7_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H202 | zenon_intro zenon_H235 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H245); [ zenon_intro zenon_H14 | zenon_intro zenon_H249 ]. % 32.93/33.15 exact (zenon_H15 zenon_H14). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H249); [ zenon_intro zenon_H1b | zenon_intro zenon_H24a ]. % 32.93/33.15 apply (zenon_L4_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H24a); [ zenon_intro zenon_H1fe | zenon_intro zenon_H21a ]. % 32.93/33.15 apply (zenon_L102_); trivial. % 32.93/33.15 apply (zenon_L136_); trivial. % 32.93/33.15 apply (zenon_L109_); trivial. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_L111_); trivial. % 32.93/33.15 apply (zenon_L137_); trivial. % 32.93/33.15 (* end of lemma zenon_L138_ *) % 32.93/33.15 assert (zenon_L139_ : (~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))) -> ((op2 (e23) (e23)) = (e23)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2a3 zenon_H84. % 32.93/33.15 cut (((op2 (e23) (e23)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H85]. % 32.93/33.15 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H1da. apply refl_equal. % 32.93/33.15 exact (zenon_H85 zenon_H84). % 32.93/33.15 (* end of lemma zenon_L139_ *) % 32.93/33.15 assert (zenon_L140_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e23) (e23)) = (e23)))\/((op2 (e23) (e23)) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (((op2 (e21) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((h4 (op1 (e10) (e10))) = (op2 (h4 (e10)) (h4 (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op2 (e20) (e20)) = (e20)))\/((op2 (e20) (e20)) = (e20))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2a4 zenon_H6f zenon_H70 zenon_H71 zenon_H5e zenon_H73 zenon_H4a zenon_H4e zenon_H54 zenon_H6a zenon_H74 zenon_H246 zenon_H22e zenon_H220 zenon_H21c zenon_H22c zenon_H23a zenon_H243 zenon_H83 zenon_H277 zenon_H24b zenon_H62 zenon_H25f zenon_H251 zenon_H268 zenon_H40 zenon_H274 zenon_H27a zenon_H87 zenon_H33 zenon_H279 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_H210 zenon_H209 zenon_H5a zenon_H1e3 zenon_H1e7 zenon_H20b zenon_H1fd zenon_H201 zenon_H1ec zenon_H211 zenon_H1dd zenon_H1dc zenon_H244 zenon_H234 zenon_H239 zenon_H297 zenon_H28b zenon_H29e zenon_H29f zenon_H245 zenon_H247 zenon_H38 zenon_H1ca zenon_H1a9 zenon_H1b6 zenon_H1c4 zenon_H1bf zenon_H1c3 zenon_H19e zenon_H19f zenon_H186 zenon_H18a zenon_H179 zenon_H195 zenon_H198 zenon_H1a0 zenon_H171 zenon_H16e zenon_H172 zenon_H173 zenon_H140 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H130 zenon_H12c zenon_H126 zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H174 zenon_H168 zenon_H175 zenon_H1cb zenon_H108 zenon_H10b zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H2a5. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 32.93/33.15 apply (zenon_L24_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H223. zenon_intro zenon_H2ad. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 32.93/33.15 apply (zenon_L86_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 32.93/33.15 apply (zenon_L9_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 32.93/33.15 apply (zenon_L112_); trivial. % 32.93/33.15 apply (zenon_L86_); trivial. % 32.93/33.15 apply (zenon_L23_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 32.93/33.15 apply (zenon_L127_); trivial. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 32.93/33.15 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 32.93/33.15 apply (zenon_L86_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 32.93/33.15 apply (zenon_L9_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 32.93/33.15 apply (zenon_L138_); trivial. % 32.93/33.15 apply (zenon_L86_); trivial. % 32.93/33.15 apply (zenon_L139_); trivial. % 32.93/33.15 (* end of lemma zenon_L140_ *) % 32.93/33.15 assert (zenon_L141_ : (~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20)))) -> ((op2 (e20) (e21)) = (e21)) -> ((op2 (e21) (e20)) = (e21)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2aa zenon_H4b zenon_H34. % 32.93/33.15 cut (((op2 (e20) (e21)) = (e21)) = ((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2aa. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H4b. % 32.93/33.15 cut (((e21) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H3d]. % 32.93/33.15 cut (((op2 (e20) (e21)) = (op2 (e20) (op2 (e21) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H2b2]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e20) (op2 (e21) (e20))) = (op2 (e20) (op2 (e21) (e20))))); [ zenon_intro zenon_H2b3 | zenon_intro zenon_H2b4 ]. % 32.93/33.15 cut (((op2 (e20) (op2 (e21) (e20))) = (op2 (e20) (op2 (e21) (e20)))) = ((op2 (e20) (e21)) = (op2 (e20) (op2 (e21) (e20))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2b2. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H2b3. % 32.93/33.15 cut (((op2 (e20) (op2 (e21) (e20))) = (op2 (e20) (op2 (e21) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H2b4]. % 32.93/33.15 cut (((op2 (e20) (op2 (e21) (e20))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2b5]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op2 (e21) (e20)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3e]. % 32.93/33.15 cut (((e20) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H12]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H12. apply refl_equal. % 32.93/33.15 exact (zenon_H3e zenon_H34). % 32.93/33.15 apply zenon_H2b4. apply refl_equal. % 32.93/33.15 apply zenon_H2b4. apply refl_equal. % 32.93/33.15 apply zenon_H3d. apply sym_equal. exact zenon_H34. % 32.93/33.15 (* end of lemma zenon_L141_ *) % 32.93/33.15 assert (zenon_L142_ : (~((op2 (e23) (e23)) = (op2 (e20) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e22) (e21)) = (e21)) -> ((op2 (e20) (e22)) = (e21)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2b6 zenon_H17 zenon_H34 zenon_H47 zenon_H59. % 32.93/33.15 cut (((op2 (e22) (e21)) = (e21)) = ((op2 (e23) (e23)) = (op2 (e20) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2b6. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H47. % 32.93/33.15 cut (((e21) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H7c]. % 32.93/33.15 cut (((op2 (e22) (e21)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2b7]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e23) (e23)) = (op2 (e23) (e23)))); [ zenon_intro zenon_H49 | zenon_intro zenon_H3c ]. % 32.93/33.15 cut (((op2 (e23) (e23)) = (op2 (e23) (e23))) = ((op2 (e22) (e21)) = (op2 (e23) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2b7. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H49. % 32.93/33.15 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 32.93/33.15 cut (((op2 (e23) (e23)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H46]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L12_); trivial. % 32.93/33.15 apply zenon_H3c. apply refl_equal. % 32.93/33.15 apply zenon_H3c. apply refl_equal. % 32.93/33.15 apply zenon_H7c. apply sym_equal. exact zenon_H59. % 32.93/33.15 (* end of lemma zenon_L142_ *) % 32.93/33.15 assert (zenon_L143_ : ((op2 (e22) (e22)) = (e21)) -> ((op2 (e20) (e22)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> ((op2 (e22) (e21)) = (e21)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H58 zenon_H59 zenon_H17 zenon_H34 zenon_H47 zenon_H5a. % 32.93/33.15 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((op2 (e20) (e22)) = (op2 (e22) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H5a. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H6b. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H207]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e22) (e22)) = (op2 (e20) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H207. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H17. % 32.93/33.15 cut (((op2 (e23) (e23)) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H2b6]. % 32.93/33.15 cut (((e21) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H5b]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (e22)) = (op2 (e22) (e22)))); [ zenon_intro zenon_H6b | zenon_intro zenon_H6c ]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22))) = ((e21) = (op2 (e22) (e22)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H5b. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H6b. % 32.93/33.15 cut (((op2 (e22) (e22)) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H6c]. % 32.93/33.15 cut (((op2 (e22) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H55]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H55 zenon_H58). % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply (zenon_L142_); trivial. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 apply zenon_H6c. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L143_ *) % 32.93/33.15 assert (zenon_L144_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e22)) = (e23))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H71 zenon_H75 zenon_H2aa zenon_H5e zenon_H2b8 zenon_H1fa zenon_H5a zenon_H34 zenon_H27e zenon_H2b9 zenon_H76 zenon_H54 zenon_H40 zenon_H4a zenon_H4e zenon_H73 zenon_H62 zenon_H17. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 32.93/33.15 exact (zenon_H75 zenon_H78). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H4b | zenon_intro zenon_H79 ]. % 32.93/33.15 apply (zenon_L141_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H59 | zenon_intro zenon_H63 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H4b | zenon_intro zenon_H7a ]. % 32.93/33.15 apply (zenon_L16_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H7a); [ zenon_intro zenon_H35 | zenon_intro zenon_H7b ]. % 32.93/33.15 exact (zenon_H76 zenon_H35). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H47 | zenon_intro zenon_H5f ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2b8); [ zenon_intro zenon_H29a | zenon_intro zenon_H2ba ]. % 32.93/33.15 exact (zenon_H1fa zenon_H29a). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2ba); [ zenon_intro zenon_H58 | zenon_intro zenon_H2bb ]. % 32.93/33.15 apply (zenon_L143_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2bb); [ zenon_intro zenon_H68 | zenon_intro zenon_H2bc ]. % 32.93/33.15 exact (zenon_H27e zenon_H68). % 32.93/33.15 exact (zenon_H2b9 zenon_H2bc). % 32.93/33.15 apply (zenon_L18_); trivial. % 32.93/33.15 apply (zenon_L19_); trivial. % 32.93/33.15 (* end of lemma zenon_L144_ *) % 32.93/33.15 assert (zenon_L145_ : ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e20)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1a zenon_H2bd zenon_H17 zenon_H2be. % 32.93/33.15 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H23d | zenon_intro zenon_H23e ]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((op2 (e21) (e21)) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2be. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H23d. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2bf]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((op2 (e21) (e23)) = (op2 (e21) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2bf. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1a. % 32.93/33.15 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (e21) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H16]. % 32.93/33.15 cut (((e20) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2c0]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e21) (e23)) = (op2 (e21) (e23)))); [ zenon_intro zenon_H23d | zenon_intro zenon_H23e ]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e21) (e23))) = ((e20) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2c0. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H23d. % 32.93/33.15 cut (((op2 (e21) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H23e]. % 32.93/33.15 cut (((op2 (e21) (e23)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H2c1]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H2c1 zenon_H2bd). % 32.93/33.15 apply zenon_H23e. apply refl_equal. % 32.93/33.15 apply zenon_H23e. apply refl_equal. % 32.93/33.15 apply (zenon_L3_); trivial. % 32.93/33.15 apply zenon_H23e. apply refl_equal. % 32.93/33.15 apply zenon_H23e. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L145_ *) % 32.93/33.15 assert (zenon_L146_ : ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e20) (e21)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1dd zenon_H69 zenon_H1f7 zenon_H1f0 zenon_H1a zenon_H4a. % 32.93/33.15 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 32.93/33.15 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((op2 (e20) (e21)) = (op2 (e22) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H4a. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H22. % 32.93/33.15 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 32.93/33.15 cut (((op2 (e22) (e21)) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2c2]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e22) (e21)) = (op2 (e20) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2c2. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1dd. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H24d]. % 32.93/33.15 cut (((e22) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H6e]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (e21)) = (op2 (e22) (e21)))); [ zenon_intro zenon_H22 | zenon_intro zenon_H23 ]. % 32.93/33.15 cut (((op2 (e22) (e21)) = (op2 (e22) (e21))) = ((e22) = (op2 (e22) (e21)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H6e. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H22. % 32.93/33.15 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 32.93/33.15 cut (((op2 (e22) (e21)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H25a]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H25a zenon_H69). % 32.93/33.15 apply zenon_H23. apply refl_equal. % 32.93/33.15 apply zenon_H23. apply refl_equal. % 32.93/33.15 apply (zenon_L114_); trivial. % 32.93/33.15 apply zenon_H23. apply refl_equal. % 32.93/33.15 apply zenon_H23. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L146_ *) % 32.93/33.15 assert (zenon_L147_ : (~((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e21) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e23)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2c3 zenon_H1f7 zenon_H1a zenon_H1f3. % 32.93/33.15 cut (((op2 (e23) (e20)) = (e22)) = ((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2c3. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1f7. % 32.93/33.15 cut (((e22) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H1f4]. % 32.93/33.15 cut (((op2 (e23) (e20)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H24e]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [ zenon_intro zenon_H24f | zenon_intro zenon_H250 ]. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e23) (e20)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H24e. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H24f. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H250]. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L88_); trivial. % 32.93/33.15 apply zenon_H250. apply refl_equal. % 32.93/33.15 apply zenon_H250. apply refl_equal. % 32.93/33.15 apply zenon_H1f4. apply sym_equal. exact zenon_H1f3. % 32.93/33.15 (* end of lemma zenon_L147_ *) % 32.93/33.15 assert (zenon_L148_ : ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e22) (e23)) = (e22)) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1dd zenon_H2c4 zenon_H1f7 zenon_H1f3 zenon_H1a zenon_H2c5. % 32.93/33.15 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H51 | zenon_intro zenon_H52 ]. % 32.93/33.15 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((op2 (e21) (e23)) = (op2 (e22) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2c5. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H51. % 32.93/33.15 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 32.93/33.15 cut (((op2 (e22) (e23)) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2c6]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e22) (e23)) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2c6. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H1dd. % 32.93/33.15 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2c3]. % 32.93/33.15 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op2 (e22) (e23)) = (op2 (e22) (e23)))); [ zenon_intro zenon_H51 | zenon_intro zenon_H52 ]. % 32.93/33.15 cut (((op2 (e22) (e23)) = (op2 (e22) (e23))) = ((e22) = (op2 (e22) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2c7. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H51. % 32.93/33.15 cut (((op2 (e22) (e23)) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H52]. % 32.93/33.15 cut (((op2 (e22) (e23)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H2c8]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H2c8 zenon_H2c4). % 32.93/33.15 apply zenon_H52. apply refl_equal. % 32.93/33.15 apply zenon_H52. apply refl_equal. % 32.93/33.15 apply (zenon_L147_); trivial. % 32.93/33.15 apply zenon_H52. apply refl_equal. % 32.93/33.15 apply zenon_H52. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L148_ *) % 32.93/33.15 assert (zenon_L149_ : (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e20) (e21)) = (e22)) -> (~((op2 (e22) (e22)) = (e22))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e23) (e20)) = (e22)) -> ((op2 (e21) (e23)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2c9 zenon_H1e7 zenon_H4a zenon_H1f0 zenon_H27e zenon_H1dd zenon_H1f7 zenon_H1f3 zenon_H1a zenon_H2c5. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H2ca ]. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H69 | zenon_intro zenon_H2cb ]. % 32.93/33.15 apply (zenon_L146_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H68 | zenon_intro zenon_H2c4 ]. % 32.93/33.15 exact (zenon_H27e zenon_H68). % 32.93/33.15 apply (zenon_L148_); trivial. % 32.93/33.15 (* end of lemma zenon_L149_ *) % 32.93/33.15 assert (zenon_L150_ : (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> ((op2 (e21) (e23)) = (e23)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H209 zenon_H21b zenon_H21f. % 32.93/33.15 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (e20) (e23)) = (op2 (e21) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H209. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H21b. % 32.93/33.15 cut (((e23) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2cc]. % 32.93/33.15 cut (((op2 (e20) (e23)) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H66]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H66. apply refl_equal. % 32.93/33.15 apply zenon_H2cc. apply sym_equal. exact zenon_H21f. % 32.93/33.15 (* end of lemma zenon_L150_ *) % 32.93/33.15 assert (zenon_L151_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e23) (e20)) = (e22)) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e22)) = (e22))) -> ((op2 (e20) (e21)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2cd zenon_H2be zenon_H17 zenon_H23a zenon_H2c5 zenon_H1a zenon_H1f7 zenon_H1dd zenon_H27e zenon_H1f0 zenon_H4a zenon_H1e7 zenon_H2c9 zenon_H209 zenon_H21b. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2cd); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2ce ]. % 32.93/33.15 apply (zenon_L145_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2ce); [ zenon_intro zenon_H23b | zenon_intro zenon_H2cf ]. % 32.93/33.15 apply (zenon_L110_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H21f ]. % 32.93/33.15 apply (zenon_L149_); trivial. % 32.93/33.15 apply (zenon_L150_); trivial. % 32.93/33.15 (* end of lemma zenon_L151_ *) % 32.93/33.15 assert (zenon_L152_ : (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> ((op2 (e22) (e23)) = (e22)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2d0 zenon_H69 zenon_H2c4. % 32.93/33.15 cut (((op2 (e22) (e21)) = (e22)) = ((op2 (e22) (e21)) = (op2 (e22) (e23)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2d0. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H69. % 32.93/33.15 cut (((e22) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H2c7]. % 32.93/33.15 cut (((op2 (e22) (e21)) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H23]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H23. apply refl_equal. % 32.93/33.15 apply zenon_H2c7. apply sym_equal. exact zenon_H2c4. % 32.93/33.15 (* end of lemma zenon_L152_ *) % 32.93/33.15 assert (zenon_L153_ : ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2d1 zenon_H1e2 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H1e7 zenon_H25f zenon_H234 zenon_H2d0 zenon_H20c zenon_H24b zenon_H14 zenon_H251 zenon_H2cd zenon_H209 zenon_H2c5 zenon_H2c9 zenon_H23a zenon_H2be zenon_H27a zenon_H211 zenon_H75 zenon_H2aa zenon_H34 zenon_H73 zenon_H5e zenon_H1fa zenon_H27e zenon_H2b8 zenon_H76 zenon_H40 zenon_H17 zenon_H4a zenon_H5a zenon_H4e zenon_H54 zenon_H62 zenon_H71. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H2b9 | zenon_intro zenon_H2c4 ]. % 32.93/33.15 apply (zenon_L144_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 32.93/33.15 exact (zenon_H1e2 zenon_H1de). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 32.93/33.15 apply (zenon_L90_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 32.93/33.15 apply (zenon_L91_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H25f); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H260 ]. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H21a | zenon_intro zenon_H27b ]. % 32.93/33.15 apply (zenon_L113_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H63 | zenon_intro zenon_H27c ]. % 32.93/33.15 apply (zenon_L19_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H20a | zenon_intro zenon_H21b ]. % 32.93/33.15 apply (zenon_L115_); trivial. % 32.93/33.15 apply (zenon_L151_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H260); [ zenon_intro zenon_H20f | zenon_intro zenon_H261 ]. % 32.93/33.15 exact (zenon_H20c zenon_H20f). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H261); [ zenon_intro zenon_H69 | zenon_intro zenon_H25b ]. % 32.93/33.15 apply (zenon_L152_); trivial. % 32.93/33.15 apply (zenon_L117_); trivial. % 32.93/33.15 (* end of lemma zenon_L153_ *) % 32.93/33.15 assert (zenon_L154_ : (~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))) -> ((op1 (e10) (e11)) = (e11)) -> ((op1 (e11) (e10)) = (e11)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H1d0 zenon_Hc4 zenon_Had. % 32.93/33.15 cut (((op1 (e10) (e11)) = (e11)) = ((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H1d0. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_Hc4. % 32.93/33.15 cut (((e11) = (op1 (e11) (e10)))); [idtac | apply NNPP; zenon_intro zenon_Hb6]. % 32.93/33.15 cut (((op1 (e10) (e11)) = (op1 (e10) (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H2d2]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op1 (e10) (op1 (e11) (e10))) = (op1 (e10) (op1 (e11) (e10))))); [ zenon_intro zenon_H2d3 | zenon_intro zenon_H2d4 ]. % 32.93/33.15 cut (((op1 (e10) (op1 (e11) (e10))) = (op1 (e10) (op1 (e11) (e10)))) = ((op1 (e10) (e11)) = (op1 (e10) (op1 (e11) (e10))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2d2. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H2d3. % 32.93/33.15 cut (((op1 (e10) (op1 (e11) (e10))) = (op1 (e10) (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H2d4]. % 32.93/33.15 cut (((op1 (e10) (op1 (e11) (e10))) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2d5]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 32.93/33.15 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H8e. apply refl_equal. % 32.93/33.15 exact (zenon_Hb7 zenon_Had). % 32.93/33.15 apply zenon_H2d4. apply refl_equal. % 32.93/33.15 apply zenon_H2d4. apply refl_equal. % 32.93/33.15 apply zenon_Hb6. apply sym_equal. exact zenon_Had. % 32.93/33.15 (* end of lemma zenon_L154_ *) % 32.93/33.15 assert (zenon_L155_ : (~((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e10) (e11)))) -> ((op1 (e13) (e10)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e10) (e11)) = (e12)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2d6 zenon_H2d7 zenon_H93 zenon_H2d8. % 32.93/33.15 cut (((op1 (e13) (e10)) = (e12)) = ((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e10) (e11)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2d6. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H2d7. % 32.93/33.15 cut (((e12) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2d9]. % 32.93/33.15 cut (((op1 (e13) (e10)) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))); [ zenon_intro zenon_H2db | zenon_intro zenon_H2dc ]. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e13) (e10)) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2da. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H2db. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))); [idtac | apply NNPP; zenon_intro zenon_H2dc]. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L52_); trivial. % 32.93/33.15 apply zenon_H2dc. apply refl_equal. % 32.93/33.15 apply zenon_H2dc. apply refl_equal. % 32.93/33.15 apply zenon_H2d9. apply sym_equal. exact zenon_H2d8. % 32.93/33.15 (* end of lemma zenon_L155_ *) % 32.93/33.15 assert (zenon_L156_ : ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e12) (e11)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e10) (e11)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H126 zenon_Hde zenon_H2d7 zenon_H2d8 zenon_H93 zenon_Hc3. % 32.93/33.15 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 32.93/33.15 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((op1 (e10) (e11)) = (op1 (e12) (e11)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_Hc3. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H9b. % 32.93/33.15 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 32.93/33.15 cut (((op1 (e12) (e11)) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2dd]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e12) (e11)) = (op1 (e10) (e11)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2dd. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H126. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e10) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2d6]. % 32.93/33.15 cut (((e12) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_He3]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op1 (e12) (e11)) = (op1 (e12) (e11)))); [ zenon_intro zenon_H9b | zenon_intro zenon_H9c ]. % 32.93/33.15 cut (((op1 (e12) (e11)) = (op1 (e12) (e11))) = ((e12) = (op1 (e12) (e11)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_He3. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H9b. % 32.93/33.15 cut (((op1 (e12) (e11)) = (op1 (e12) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H9c]. % 32.93/33.15 cut (((op1 (e12) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H194]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H194 zenon_Hde). % 32.93/33.15 apply zenon_H9c. apply refl_equal. % 32.93/33.15 apply zenon_H9c. apply refl_equal. % 32.93/33.15 apply (zenon_L155_); trivial. % 32.93/33.15 apply zenon_H9c. apply refl_equal. % 32.93/33.15 apply zenon_H9c. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L156_ *) % 32.93/33.15 assert (zenon_L157_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((op1 (e11) (e10)) = (e11)) -> ((op1 (e12) (e11)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e12) (e11)) = (e12)) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2de zenon_H92 zenon_H90 zenon_Had zenon_Hc0 zenon_Hc3 zenon_H93 zenon_H2d7 zenon_Hde zenon_H126 zenon_H12d zenon_H179. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2de); [ zenon_intro zenon_H94 | zenon_intro zenon_H2df ]. % 32.93/33.15 apply (zenon_L27_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2df); [ zenon_intro zenon_Hc4 | zenon_intro zenon_H2e0 ]. % 32.93/33.15 apply (zenon_L36_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2e0); [ zenon_intro zenon_H2d8 | zenon_intro zenon_H178 ]. % 32.93/33.15 apply (zenon_L156_); trivial. % 32.93/33.15 apply (zenon_L67_); trivial. % 32.93/33.15 (* end of lemma zenon_L157_ *) % 32.93/33.15 assert (zenon_L158_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e12) (e11)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((op1 (e10) (e12)) = (e11)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2e1 zenon_H2e2 zenon_H140 zenon_H1bf zenon_Hcd zenon_Hb9 zenon_H179 zenon_H12d zenon_H126 zenon_Hde zenon_H93 zenon_Hc3 zenon_Had zenon_H92 zenon_H2de zenon_Hef zenon_H2e3 zenon_Hc7 zenon_H90. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H2e4 ]. % 32.93/33.15 exact (zenon_H2e2 zenon_H2e5). % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H141 | zenon_intro zenon_H2e6 ]. % 32.93/33.15 apply (zenon_L57_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H2d7 ]. % 32.93/33.15 apply (zenon_L84_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_Hcd); [ zenon_intro zenon_Hb8 | zenon_intro zenon_Hcf ]. % 32.93/33.15 apply (zenon_L34_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_Hcf); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hd0 ]. % 32.93/33.15 apply (zenon_L157_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_Hd0); [ zenon_intro zenon_Hd1 | zenon_intro zenon_Hc8 ]. % 32.93/33.15 cut (((op1 (e10) (e12)) = (e11)) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2e3. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_Hef. % 32.93/33.15 cut (((e11) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H2e7]. % 32.93/33.15 cut (((op1 (e10) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H136]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_H136. apply refl_equal. % 32.93/33.15 apply zenon_H2e7. apply sym_equal. exact zenon_Hd1. % 32.93/33.15 apply (zenon_L37_); trivial. % 32.93/33.15 (* end of lemma zenon_L158_ *) % 32.93/33.15 assert (zenon_L159_ : ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (e10)) = (e11))) -> (~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H172 zenon_Hea zenon_H1d0 zenon_Had zenon_H2e1 zenon_Hb9 zenon_H2de zenon_H179 zenon_Hde zenon_Hc3 zenon_H92 zenon_H2e3 zenon_Hc7 zenon_Hcd zenon_H1bf zenon_H93 zenon_H126 zenon_H140 zenon_H2e2 zenon_Hd7 zenon_He6 zenon_H90. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.15 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.15 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 32.93/33.15 exact (zenon_Hea zenon_Hed). % 32.93/33.15 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 32.93/33.15 apply (zenon_L154_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 32.93/33.15 apply (zenon_L158_); trivial. % 32.93/33.15 apply (zenon_L41_); trivial. % 32.93/33.15 (* end of lemma zenon_L159_ *) % 32.93/33.15 assert (zenon_L160_ : ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e10)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H93 zenon_H2e8 zenon_H90 zenon_H2e9. % 32.93/33.15 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H16b | zenon_intro zenon_H16c ]. % 32.93/33.15 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((op1 (e11) (e11)) = (op1 (e11) (e13)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2e9. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H16b. % 32.93/33.15 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 32.93/33.15 cut (((op1 (e11) (e13)) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2ea]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = ((op1 (e11) (e13)) = (op1 (e11) (e11)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2ea. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H93. % 32.93/33.15 cut (((op1 (op1 (e13) (e13)) (op1 (e13) (e13))) = (op1 (e11) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H8f]. % 32.93/33.15 cut (((e10) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2eb]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op1 (e11) (e13)) = (op1 (e11) (e13)))); [ zenon_intro zenon_H16b | zenon_intro zenon_H16c ]. % 32.93/33.15 cut (((op1 (e11) (e13)) = (op1 (e11) (e13))) = ((e10) = (op1 (e11) (e13)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2eb. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H16b. % 32.93/33.15 cut (((op1 (e11) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H16c]. % 32.93/33.15 cut (((op1 (e11) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H2ec]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H2ec zenon_H2e8). % 32.93/33.15 apply zenon_H16c. apply refl_equal. % 32.93/33.15 apply zenon_H16c. apply refl_equal. % 32.93/33.15 apply (zenon_L26_); trivial. % 32.93/33.15 apply zenon_H16c. apply refl_equal. % 32.93/33.15 apply zenon_H16c. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L160_ *) % 32.93/33.15 assert (zenon_L161_ : (~((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e11) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e11) (e13)) = (e12)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2ed zenon_H2d7 zenon_H93 zenon_H151. % 32.93/33.15 cut (((op1 (e13) (e10)) = (e12)) = ((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e11) (e13)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2ed. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H2d7. % 32.93/33.15 cut (((e12) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H19a]. % 32.93/33.15 cut (((op1 (e13) (e10)) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))); [idtac | apply NNPP; zenon_intro zenon_H2da]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))); [ zenon_intro zenon_H2db | zenon_intro zenon_H2dc ]. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e13) (e10)) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2da. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H2db. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))))); [idtac | apply NNPP; zenon_intro zenon_H2dc]. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 32.93/33.15 congruence. % 32.93/33.15 apply (zenon_L52_); trivial. % 32.93/33.15 apply zenon_H2dc. apply refl_equal. % 32.93/33.15 apply zenon_H2dc. apply refl_equal. % 32.93/33.15 apply zenon_H19a. apply sym_equal. exact zenon_H151. % 32.93/33.15 (* end of lemma zenon_L161_ *) % 32.93/33.15 assert (zenon_L162_ : ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e12) (e13)) = (e12)) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e11) (e13)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> False). % 32.93/33.15 do 0 intro. intros zenon_H126 zenon_H2ee zenon_H2d7 zenon_H151 zenon_H93 zenon_H2ef. % 32.93/33.15 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 32.93/33.15 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((op1 (e11) (e13)) = (op1 (e12) (e13)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2ef. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_Hca. % 32.93/33.15 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 32.93/33.15 cut (((op1 (e12) (e13)) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2f0]. % 32.93/33.15 congruence. % 32.93/33.15 cut (((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e12) (e13)) = (op1 (e11) (e13)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2f0. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H126. % 32.93/33.15 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2ed]. % 32.93/33.15 cut (((e12) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2f1]. % 32.93/33.15 congruence. % 32.93/33.15 elim (classic ((op1 (e12) (e13)) = (op1 (e12) (e13)))); [ zenon_intro zenon_Hca | zenon_intro zenon_Hcb ]. % 32.93/33.15 cut (((op1 (e12) (e13)) = (op1 (e12) (e13))) = ((e12) = (op1 (e12) (e13)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H2f1. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_Hca. % 32.93/33.15 cut (((op1 (e12) (e13)) = (op1 (e12) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hcb]. % 32.93/33.15 cut (((op1 (e12) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H2f2]. % 32.93/33.15 congruence. % 32.93/33.15 exact (zenon_H2f2 zenon_H2ee). % 32.93/33.15 apply zenon_Hcb. apply refl_equal. % 32.93/33.15 apply zenon_Hcb. apply refl_equal. % 32.93/33.15 apply (zenon_L161_); trivial. % 32.93/33.15 apply zenon_Hcb. apply refl_equal. % 32.93/33.15 apply zenon_Hcb. apply refl_equal. % 32.93/33.15 (* end of lemma zenon_L162_ *) % 32.93/33.15 assert (zenon_L163_ : (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> ((op1 (e11) (e13)) = (e13)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H198 zenon_H14d zenon_H152. % 32.93/33.15 cut (((op1 (e10) (e13)) = (e13)) = ((op1 (e10) (e13)) = (op1 (e11) (e13)))). % 32.93/33.15 intro zenon_D_pnotp. % 32.93/33.15 apply zenon_H198. % 32.93/33.15 rewrite <- zenon_D_pnotp. % 32.93/33.15 exact zenon_H14d. % 32.93/33.15 cut (((e13) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H2f3]. % 32.93/33.15 cut (((op1 (e10) (e13)) = (op1 (e10) (e13)))); [idtac | apply NNPP; zenon_intro zenon_Hdb]. % 32.93/33.15 congruence. % 32.93/33.15 apply zenon_Hdb. apply refl_equal. % 32.93/33.15 apply zenon_H2f3. apply sym_equal. exact zenon_H152. % 32.93/33.15 (* end of lemma zenon_L163_ *) % 32.93/33.15 assert (zenon_L164_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e13) (e10)) = (e12)) -> ((op1 (e12) (e13)) = (e12)) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> False). % 32.93/33.15 do 0 intro. intros zenon_H2f4 zenon_H2e9 zenon_H90 zenon_H168 zenon_H2ef zenon_H93 zenon_H2d7 zenon_H2ee zenon_H126 zenon_H198 zenon_H14d. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2e8 | zenon_intro zenon_H2f5 ]. % 32.93/33.15 apply (zenon_L160_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H169 | zenon_intro zenon_H2f6 ]. % 32.93/33.15 apply (zenon_L64_); trivial. % 32.93/33.15 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H151 | zenon_intro zenon_H152 ]. % 32.93/33.15 apply (zenon_L162_); trivial. % 32.93/33.15 apply (zenon_L163_); trivial. % 32.93/33.15 (* end of lemma zenon_L164_ *) % 32.93/33.15 assert (zenon_L165_ : (~((op1 (e10) (e10)) = (e11))) -> (~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e12) (e12)) = (e12))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (e12))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_Hea zenon_H1d0 zenon_Had zenon_H18b zenon_H179 zenon_Hf9 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H19c zenon_He6 zenon_Hd7 zenon_Hcd zenon_Hc7 zenon_H2e3 zenon_H92 zenon_Hc3 zenon_H2de zenon_Hb9 zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H93 zenon_H126 zenon_H140 zenon_H2e2 zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.16 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 32.93/33.16 exact (zenon_Hea zenon_Hed). % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 32.93/33.16 apply (zenon_L154_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H2e4 ]. % 32.93/33.16 exact (zenon_H2e2 zenon_H2e5). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H141 | zenon_intro zenon_H2e6 ]. % 32.93/33.16 apply (zenon_L57_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H2d7 ]. % 32.93/33.16 apply (zenon_L84_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H18d | zenon_intro zenon_H1a4 ]. % 32.93/33.16 exact (zenon_H18b zenon_H18d). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H178 | zenon_intro zenon_H1a5 ]. % 32.93/33.16 apply (zenon_L67_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H17c | zenon_intro zenon_H14d ]. % 32.93/33.16 apply (zenon_L68_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H2f8 ]. % 32.93/33.16 apply (zenon_L84_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f9 ]. % 32.93/33.16 apply (zenon_L159_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2ee ]. % 32.93/33.16 exact (zenon_H19c zenon_Hdd). % 32.93/33.16 apply (zenon_L164_); trivial. % 32.93/33.16 apply (zenon_L41_); trivial. % 32.93/33.16 (* end of lemma zenon_L165_ *) % 32.93/33.16 assert (zenon_L166_ : (~((h4 (e11)) = (e21))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H2fa zenon_H2fb zenon_H17. % 32.93/33.16 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (e11)) = (e21))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H2fa. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H2fb. % 32.93/33.16 cut (((op2 (e23) (e23)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H18]. % 32.93/33.16 cut (((h4 (e11)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H2fc]. % 32.93/33.16 congruence. % 32.93/33.16 apply zenon_H2fc. apply refl_equal. % 32.93/33.16 apply zenon_H18. apply sym_equal. exact zenon_H17. % 32.93/33.16 (* end of lemma zenon_L166_ *) % 32.93/33.16 assert (zenon_L167_ : (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op1 (e10) (e11)) = (e12)) -> ((op2 (e20) (e21)) = (e22)) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H2fd zenon_H2fe zenon_H2d8 zenon_H1f0 zenon_H1dd zenon_H108 zenon_H1a zenon_H2fb zenon_H17. % 32.93/33.16 cut (((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H2fd. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H2fe. % 32.93/33.16 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H2ff]. % 32.93/33.16 cut (((h4 (e12)) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H300]. % 32.93/33.16 congruence. % 32.93/33.16 elim (classic ((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [ zenon_intro zenon_H301 | zenon_intro zenon_H302 ]. % 32.93/33.16 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11)))) = ((h4 (e12)) = (h4 (op1 (e10) (e11))))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H300. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H301. % 32.93/33.16 cut (((h4 (op1 (e10) (e11))) = (h4 (op1 (e10) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H302]. % 32.93/33.16 cut (((h4 (op1 (e10) (e11))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H303]. % 32.93/33.16 congruence. % 32.93/33.16 cut (((op1 (e10) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H304]. % 32.93/33.16 congruence. % 32.93/33.16 exact (zenon_H304 zenon_H2d8). % 32.93/33.16 apply zenon_H302. apply refl_equal. % 32.93/33.16 apply zenon_H302. apply refl_equal. % 32.93/33.16 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H305 | zenon_intro zenon_H306 ]. % 32.93/33.16 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e10)) (h4 (e11))))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H2ff. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H305. % 32.93/33.16 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H306]. % 32.93/33.16 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H307]. % 32.93/33.16 congruence. % 32.93/33.16 cut (((op2 (e20) (e21)) = (e22)) = ((op2 (h4 (e10)) (h4 (e11))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H307. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H1f0. % 32.93/33.16 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 32.93/33.16 cut (((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H309]. % 32.93/33.16 congruence. % 32.93/33.16 elim (classic ((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [ zenon_intro zenon_H305 | zenon_intro zenon_H306 ]. % 32.93/33.16 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11)))) = ((op2 (e20) (e21)) = (op2 (h4 (e10)) (h4 (e11))))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H309. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H305. % 32.93/33.16 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (h4 (e10)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H306]. % 32.93/33.16 cut (((op2 (h4 (e10)) (h4 (e11))) = (op2 (e20) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H30a]. % 32.93/33.16 congruence. % 32.93/33.16 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 32.93/33.16 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 32.93/33.16 congruence. % 32.93/33.16 apply (zenon_L47_); trivial. % 32.93/33.16 apply (zenon_L166_); trivial. % 32.93/33.16 apply zenon_H306. apply refl_equal. % 32.93/33.16 apply zenon_H306. apply refl_equal. % 32.93/33.16 exact (zenon_H308 zenon_H1dd). % 32.93/33.16 apply zenon_H306. apply refl_equal. % 32.93/33.16 apply zenon_H306. apply refl_equal. % 32.93/33.16 (* end of lemma zenon_L167_ *) % 32.93/33.16 assert (zenon_L168_ : ((op1 (e12) (e12)) = (e12)) -> ((op1 (e10) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> False). % 32.93/33.16 do 0 intro. intros zenon_Hdd zenon_H30b zenon_H2e3. % 32.93/33.16 elim (classic ((op1 (e12) (e12)) = (op1 (e12) (e12)))); [ zenon_intro zenon_He0 | zenon_intro zenon_He1 ]. % 32.93/33.16 cut (((op1 (e12) (e12)) = (op1 (e12) (e12))) = ((op1 (e10) (e12)) = (op1 (e12) (e12)))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H2e3. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_He0. % 32.93/33.16 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 32.93/33.16 cut (((op1 (e12) (e12)) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H30c]. % 32.93/33.16 congruence. % 32.93/33.16 cut (((op1 (e12) (e12)) = (e12)) = ((op1 (e12) (e12)) = (op1 (e10) (e12)))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H30c. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_Hdd. % 32.93/33.16 cut (((e12) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H30d]. % 32.93/33.16 cut (((op1 (e12) (e12)) = (op1 (e12) (e12)))); [idtac | apply NNPP; zenon_intro zenon_He1]. % 32.93/33.16 congruence. % 32.93/33.16 apply zenon_He1. apply refl_equal. % 32.93/33.16 apply zenon_H30d. apply sym_equal. exact zenon_H30b. % 32.93/33.16 apply zenon_He1. apply refl_equal. % 32.93/33.16 apply zenon_He1. apply refl_equal. % 32.93/33.16 (* end of lemma zenon_L168_ *) % 32.93/33.16 assert (zenon_L169_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e13)) -> False). % 32.93/33.16 do 0 intro. intros zenon_H2f4 zenon_H2e9 zenon_H93 zenon_H90 zenon_H168 zenon_H199 zenon_H198 zenon_H14d. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2e8 | zenon_intro zenon_H2f5 ]. % 32.93/33.16 apply (zenon_L160_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H169 | zenon_intro zenon_H2f6 ]. % 32.93/33.16 apply (zenon_L64_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H151 | zenon_intro zenon_H152 ]. % 32.93/33.16 apply (zenon_L75_); trivial. % 32.93/33.16 apply (zenon_L163_); trivial. % 32.93/33.16 (* end of lemma zenon_L169_ *) % 32.93/33.16 assert (zenon_L170_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H19f zenon_H18b zenon_H179 zenon_H12d zenon_Hf9 zenon_Hef zenon_H2f4 zenon_H2e9 zenon_H93 zenon_H90 zenon_H168 zenon_H199 zenon_H198. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H18d | zenon_intro zenon_H1a4 ]. % 32.93/33.16 exact (zenon_H18b zenon_H18d). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H178 | zenon_intro zenon_H1a5 ]. % 32.93/33.16 apply (zenon_L67_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H17c | zenon_intro zenon_H14d ]. % 32.93/33.16 apply (zenon_L68_); trivial. % 32.93/33.16 apply (zenon_L169_); trivial. % 32.93/33.16 (* end of lemma zenon_L170_ *) % 32.93/33.16 assert (zenon_L171_ : ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e10) (e10)) = (e11))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H172 zenon_H1e2 zenon_He6 zenon_Hd7 zenon_H2e2 zenon_H2fd zenon_H2fe zenon_H17 zenon_H2fb zenon_H1a zenon_H108 zenon_H1dd zenon_H2e3 zenon_Hdd zenon_H19f zenon_H2e9 zenon_H93 zenon_H168 zenon_H198 zenon_H2f4 zenon_Hf9 zenon_H179 zenon_H18b zenon_H30e zenon_Hb9 zenon_Had zenon_Hc3 zenon_Hce zenon_Hc7 zenon_Hcd zenon_Hea zenon_H5a zenon_H68 zenon_H20b zenon_H209 zenon_H1ec zenon_H20c zenon_H1e3 zenon_H210 zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.16 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H1de | zenon_intro zenon_H212 ]. % 32.93/33.16 exact (zenon_H1e2 zenon_H1de). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H213 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 32.93/33.16 exact (zenon_Hea zenon_Hed). % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 32.93/33.16 apply (zenon_L38_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H30f ]. % 32.93/33.16 exact (zenon_H2e2 zenon_H2e5). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H2d8 | zenon_intro zenon_H310 ]. % 32.93/33.16 apply (zenon_L167_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_H30b | zenon_intro zenon_H199 ]. % 32.93/33.16 apply (zenon_L168_); trivial. % 32.93/33.16 apply (zenon_L170_); trivial. % 32.93/33.16 apply (zenon_L41_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H206 | zenon_intro zenon_H20a ]. % 32.93/33.16 apply (zenon_L99_); trivial. % 32.93/33.16 apply (zenon_L101_); trivial. % 32.93/33.16 (* end of lemma zenon_L171_ *) % 32.93/33.16 assert (zenon_L172_ : ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))) -> ((e11) = (op1 (e13) (e13))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_He9 zenon_H140 zenon_H126 zenon_H1bf zenon_H92 zenon_H2de zenon_H2e1 zenon_H1d0 zenon_H90 zenon_H210 zenon_H1e3 zenon_H20c zenon_H1ec zenon_H209 zenon_H20b zenon_H68 zenon_H5a zenon_Hea zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Had zenon_Hb9 zenon_H30e zenon_H18b zenon_H179 zenon_Hf9 zenon_H2f4 zenon_H198 zenon_H168 zenon_H93 zenon_H2e9 zenon_H19f zenon_Hdd zenon_H2e3 zenon_H1dd zenon_H108 zenon_H1a zenon_H2fb zenon_H17 zenon_H2fe zenon_H2fd zenon_H2e2 zenon_Hd7 zenon_He6 zenon_H1e2 zenon_H172. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 32.93/33.16 apply (zenon_L171_); trivial. % 32.93/33.16 apply (zenon_L159_); trivial. % 32.93/33.16 (* end of lemma zenon_L172_ *) % 32.93/33.16 assert (zenon_L173_ : (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> ((op1 (e10) (e12)) = (e10)) -> False). % 32.93/33.16 do 0 intro. intros zenon_H311 zenon_H104 zenon_H131. % 32.93/33.16 cut (((op1 (e10) (e10)) = (e10)) = ((op1 (e10) (e10)) = (op1 (e10) (e12)))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H311. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H104. % 32.93/33.16 cut (((e10) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H134]. % 32.93/33.16 cut (((op1 (e10) (e10)) = (op1 (e10) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H197]. % 32.93/33.16 congruence. % 32.93/33.16 apply zenon_H197. apply refl_equal. % 32.93/33.16 apply zenon_H134. apply sym_equal. exact zenon_H131. % 32.93/33.16 (* end of lemma zenon_L173_ *) % 32.93/33.16 assert (zenon_L174_ : ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12)))) -> (~((e12) = (e13))) -> ((op1 (e10) (e13)) = (e10)) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> False). % 32.93/33.16 do 0 intro. intros zenon_Hb1 zenon_H175 zenon_H168 zenon_H15f zenon_Hf9 zenon_H161 zenon_H156 zenon_H153 zenon_H14c zenon_H14e zenon_H160 zenon_Hdd zenon_H145 zenon_H126 zenon_H140 zenon_H174 zenon_H16e zenon_H171 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.16 apply (zenon_L30_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H13b | zenon_intro zenon_H169 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H174); [ zenon_intro zenon_Hfb | zenon_intro zenon_Hfa ]. % 32.93/33.16 apply (zenon_L63_); trivial. % 32.93/33.16 apply (zenon_L45_); trivial. % 32.93/33.16 apply (zenon_L64_); trivial. % 32.93/33.16 apply (zenon_L65_); trivial. % 32.93/33.16 (* end of lemma zenon_L174_ *) % 32.93/33.16 assert (zenon_L175_ : ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e12)) = (e10)) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> False). % 32.93/33.16 do 0 intro. intros zenon_Hb1 zenon_H171 zenon_H16e zenon_H172 zenon_H130 zenon_H12c zenon_H126 zenon_H128 zenon_H11d zenon_H131 zenon_H132 zenon_H139 zenon_H168 zenon_H175 zenon_Hac zenon_He5 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.16 apply (zenon_L30_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Heb | zenon_intro zenon_Hae ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H13b | zenon_intro zenon_H169 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.16 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.16 apply (zenon_L56_); trivial. % 32.93/33.16 apply (zenon_L64_); trivial. % 32.93/33.16 apply (zenon_L65_); trivial. % 32.93/33.16 apply (zenon_L31_); trivial. % 32.93/33.16 (* end of lemma zenon_L175_ *) % 32.93/33.16 assert (zenon_L176_ : ((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13))))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (~((e11) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H1ce zenon_Hfd zenon_H311 zenon_H2f7 zenon_H2ef zenon_H312 zenon_H195 zenon_H313 zenon_He5 zenon_Hac zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_Hb1 zenon_H172 zenon_H1e2 zenon_He6 zenon_Hd7 zenon_H2fd zenon_H2fe zenon_H17 zenon_H2fb zenon_H1a zenon_H108 zenon_H1dd zenon_H2e3 zenon_H19f zenon_H2e9 zenon_H168 zenon_H198 zenon_H2f4 zenon_H179 zenon_H30e zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_H5a zenon_H68 zenon_H20b zenon_H209 zenon_H1ec zenon_H20c zenon_H1e3 zenon_H210 zenon_H2e1 zenon_H2de zenon_H1bf zenon_H126 zenon_H140 zenon_He9 zenon_H92 zenon_H93 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_H175 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H174 zenon_H16e zenon_H171 zenon_H19e zenon_He4 zenon_Hf9 zenon_H90. % 32.93/33.16 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 32.93/33.16 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 32.93/33.16 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.16 apply (zenon_L30_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 32.93/33.16 apply (zenon_L165_); trivial. % 32.93/33.16 apply (zenon_L172_); trivial. % 32.93/33.16 apply (zenon_L74_); trivial. % 32.93/33.16 apply (zenon_L173_); trivial. % 32.93/33.16 apply (zenon_L27_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 32.93/33.16 apply (zenon_L32_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.16 apply (zenon_L30_); trivial. % 32.93/33.16 apply (zenon_L172_); trivial. % 32.93/33.16 apply (zenon_L174_); trivial. % 32.93/33.16 apply (zenon_L175_); trivial. % 32.93/33.16 apply (zenon_L27_); trivial. % 32.93/33.16 apply (zenon_L45_); trivial. % 32.93/33.16 (* end of lemma zenon_L176_ *) % 32.93/33.16 assert (zenon_L177_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10)))) -> ((op1 (e10) (e12)) = (e12)) -> False). % 32.93/33.16 do 0 intro. intros zenon_H2e1 zenon_H2e2 zenon_H140 zenon_H93 zenon_H126 zenon_H1bf zenon_H1d6 zenon_H30b. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H2e4 ]. % 32.93/33.16 exact (zenon_H2e2 zenon_H2e5). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H141 | zenon_intro zenon_H2e6 ]. % 32.93/33.16 apply (zenon_L57_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H2d7 ]. % 32.93/33.16 apply (zenon_L84_); trivial. % 32.93/33.16 cut (((op1 (e10) (e12)) = (e12)) = ((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10)))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H1d6. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H30b. % 32.93/33.16 cut (((e12) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H314]. % 32.93/33.16 cut (((op1 (e10) (e12)) = (op1 (e10) (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H315]. % 32.93/33.16 congruence. % 32.93/33.16 elim (classic ((op1 (e10) (op1 (e13) (e10))) = (op1 (e10) (op1 (e13) (e10))))); [ zenon_intro zenon_H316 | zenon_intro zenon_H317 ]. % 32.93/33.16 cut (((op1 (e10) (op1 (e13) (e10))) = (op1 (e10) (op1 (e13) (e10)))) = ((op1 (e10) (e12)) = (op1 (e10) (op1 (e13) (e10))))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H315. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H316. % 32.93/33.16 cut (((op1 (e10) (op1 (e13) (e10))) = (op1 (e10) (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H317]. % 32.93/33.16 cut (((op1 (e10) (op1 (e13) (e10))) = (op1 (e10) (e12)))); [idtac | apply NNPP; zenon_intro zenon_H318]. % 32.93/33.16 congruence. % 32.93/33.16 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H319]. % 32.93/33.16 cut (((e10) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H8e]. % 32.93/33.16 congruence. % 32.93/33.16 apply zenon_H8e. apply refl_equal. % 32.93/33.16 exact (zenon_H319 zenon_H2d7). % 32.93/33.16 apply zenon_H317. apply refl_equal. % 32.93/33.16 apply zenon_H317. apply refl_equal. % 32.93/33.16 apply zenon_H314. apply sym_equal. exact zenon_H2d7. % 32.93/33.16 (* end of lemma zenon_L177_ *) % 32.93/33.16 assert (zenon_L178_ : (~((op1 (e11) (op1 (e13) (e11))) = (op1 (e11) (e13)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 32.93/33.16 do 0 intro. intros zenon_H31a zenon_H12d. % 32.93/33.16 cut (((op1 (e13) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 32.93/33.16 cut (((e11) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hf8]. % 32.93/33.16 congruence. % 32.93/33.16 apply zenon_Hf8. apply refl_equal. % 32.93/33.16 exact (zenon_H31b zenon_H12d). % 32.93/33.16 (* end of lemma zenon_L178_ *) % 32.93/33.16 assert (zenon_L179_ : (~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11)))) -> ((op1 (e11) (e13)) = (e13)) -> ((op1 (e13) (e11)) = (e13)) -> False). % 32.93/33.16 do 0 intro. intros zenon_H1d8 zenon_H152 zenon_H12d. % 32.93/33.16 cut (((op1 (e11) (e13)) = (e13)) = ((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11)))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H1d8. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H152. % 32.93/33.16 cut (((e13) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H188]. % 32.93/33.16 cut (((op1 (e11) (e13)) = (op1 (e11) (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H31c]. % 32.93/33.16 congruence. % 32.93/33.16 elim (classic ((op1 (e11) (op1 (e13) (e11))) = (op1 (e11) (op1 (e13) (e11))))); [ zenon_intro zenon_H31d | zenon_intro zenon_H31e ]. % 32.93/33.16 cut (((op1 (e11) (op1 (e13) (e11))) = (op1 (e11) (op1 (e13) (e11)))) = ((op1 (e11) (e13)) = (op1 (e11) (op1 (e13) (e11))))). % 32.93/33.16 intro zenon_D_pnotp. % 32.93/33.16 apply zenon_H31c. % 32.93/33.16 rewrite <- zenon_D_pnotp. % 32.93/33.16 exact zenon_H31d. % 32.93/33.16 cut (((op1 (e11) (op1 (e13) (e11))) = (op1 (e11) (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H31e]. % 32.93/33.16 cut (((op1 (e11) (op1 (e13) (e11))) = (op1 (e11) (e13)))); [idtac | apply NNPP; zenon_intro zenon_H31a]. % 32.93/33.16 congruence. % 32.93/33.16 apply (zenon_L178_); trivial. % 32.93/33.16 apply zenon_H31e. apply refl_equal. % 32.93/33.16 apply zenon_H31e. apply refl_equal. % 32.93/33.16 apply zenon_H188. apply sym_equal. exact zenon_H12d. % 32.93/33.16 (* end of lemma zenon_L179_ *) % 32.93/33.16 assert (zenon_L180_ : (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 32.93/33.16 do 0 intro. intros zenon_H2f4 zenon_H2e9 zenon_H93 zenon_H90 zenon_H168 zenon_H199 zenon_H198 zenon_H1d8 zenon_H12d. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f4); [ zenon_intro zenon_H2e8 | zenon_intro zenon_H2f5 ]. % 32.93/33.16 apply (zenon_L160_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f5); [ zenon_intro zenon_H169 | zenon_intro zenon_H2f6 ]. % 32.93/33.16 apply (zenon_L64_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f6); [ zenon_intro zenon_H151 | zenon_intro zenon_H152 ]. % 32.93/33.16 apply (zenon_L75_); trivial. % 32.93/33.16 apply (zenon_L179_); trivial. % 32.93/33.16 (* end of lemma zenon_L180_ *) % 32.93/33.16 assert (zenon_L181_ : ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (e10)) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((op1 (e12) (e11)) = (e12)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H172 zenon_H2e2 zenon_H2e1 zenon_Hde zenon_Hc3 zenon_H1bf zenon_H93 zenon_H126 zenon_H140 zenon_H1d6 zenon_H2f4 zenon_H1d8 zenon_H198 zenon_H168 zenon_H2e9 zenon_H30e zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.16 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H30f ]. % 32.93/33.16 exact (zenon_H2e2 zenon_H2e5). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H2d8 | zenon_intro zenon_H310 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H2e4 ]. % 32.93/33.16 exact (zenon_H2e2 zenon_H2e5). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H141 | zenon_intro zenon_H2e6 ]. % 32.93/33.16 apply (zenon_L57_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H2d7 ]. % 32.93/33.16 apply (zenon_L84_); trivial. % 32.93/33.16 apply (zenon_L156_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_H30b | zenon_intro zenon_H199 ]. % 32.93/33.16 apply (zenon_L177_); trivial. % 32.93/33.16 apply (zenon_L180_); trivial. % 32.93/33.16 (* end of lemma zenon_L181_ *) % 32.93/33.16 assert (zenon_L182_ : (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> (~((e11) = (e13))) -> ((op1 (e10) (e12)) = (e11)) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H2e1 zenon_H2e2 zenon_H140 zenon_H1bf zenon_H19f zenon_H18b zenon_H179 zenon_H12d zenon_Hf9 zenon_Hef zenon_H2f4 zenon_H2e9 zenon_H90 zenon_H168 zenon_H2ef zenon_H93 zenon_H2ee zenon_H126 zenon_H198. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e1); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H2e4 ]. % 32.93/33.16 exact (zenon_H2e2 zenon_H2e5). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e4); [ zenon_intro zenon_H141 | zenon_intro zenon_H2e6 ]. % 32.93/33.16 apply (zenon_L57_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2e6); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H2d7 ]. % 32.93/33.16 apply (zenon_L84_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H18d | zenon_intro zenon_H1a4 ]. % 32.93/33.16 exact (zenon_H18b zenon_H18d). % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H178 | zenon_intro zenon_H1a5 ]. % 32.93/33.16 apply (zenon_L67_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H17c | zenon_intro zenon_H14d ]. % 32.93/33.16 apply (zenon_L68_); trivial. % 32.93/33.16 apply (zenon_L164_); trivial. % 32.93/33.16 (* end of lemma zenon_L182_ *) % 32.93/33.16 assert (zenon_L183_ : ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e12) (e13)) = (e12)) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H172 zenon_Hea zenon_Hcd zenon_Hc7 zenon_Hce zenon_Hc3 zenon_Had zenon_Hb9 zenon_H2e1 zenon_H18b zenon_H179 zenon_Hf9 zenon_H2f4 zenon_H198 zenon_H2ee zenon_H2ef zenon_H168 zenon_H2e9 zenon_H19f zenon_H1bf zenon_H93 zenon_H126 zenon_H140 zenon_H2e2 zenon_Hd7 zenon_He6 zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 32.93/33.16 apply zenon_H91. apply sym_equal. exact zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 32.93/33.16 exact (zenon_Hea zenon_Hed). % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 32.93/33.16 apply (zenon_L38_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 32.93/33.16 apply (zenon_L182_); trivial. % 32.93/33.16 apply (zenon_L41_); trivial. % 32.93/33.16 (* end of lemma zenon_L183_ *) % 32.93/33.16 assert (zenon_L184_ : (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11)))) -> (~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10)))) -> (~((op1 (e12) (e12)) = (e12))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((e11) = (op1 (e13) (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H2f7 zenon_H30e zenon_H1d8 zenon_H1d6 zenon_H19c zenon_H172 zenon_Hea zenon_Hcd zenon_Hc7 zenon_Hce zenon_Hc3 zenon_Had zenon_Hb9 zenon_H2e1 zenon_H18b zenon_H179 zenon_Hf9 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H19f zenon_H1bf zenon_H93 zenon_H126 zenon_H140 zenon_H2e2 zenon_Hd7 zenon_He6 zenon_H90. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f7); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H2f8 ]. % 32.93/33.16 apply (zenon_L84_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f8); [ zenon_intro zenon_Hde | zenon_intro zenon_H2f9 ]. % 32.93/33.16 apply (zenon_L181_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H2f9); [ zenon_intro zenon_Hdd | zenon_intro zenon_H2ee ]. % 32.93/33.16 exact (zenon_H19c zenon_Hdd). % 32.93/33.16 apply (zenon_L183_); trivial. % 32.93/33.16 (* end of lemma zenon_L184_ *) % 32.93/33.16 assert (zenon_L185_ : ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11)))) -> (~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((e11) = (op1 (e13) (e13))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> (~((op1 (e10) (e10)) = (e12))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> False). % 32.93/33.16 do 0 intro. intros zenon_He9 zenon_H1d8 zenon_H1d6 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e1 zenon_H90 zenon_H210 zenon_H1e3 zenon_H20c zenon_H1ec zenon_H209 zenon_H20b zenon_H68 zenon_H5a zenon_Hea zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Had zenon_Hb9 zenon_H30e zenon_H18b zenon_H179 zenon_Hf9 zenon_H2f4 zenon_H198 zenon_H168 zenon_H93 zenon_H2e9 zenon_H19f zenon_Hdd zenon_H2e3 zenon_H1dd zenon_H108 zenon_H1a zenon_H2fb zenon_H17 zenon_H2fe zenon_H2fd zenon_H2e2 zenon_Hd7 zenon_He6 zenon_H1e2 zenon_H172. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 32.93/33.16 apply (zenon_L171_); trivial. % 32.93/33.16 apply (zenon_L181_); trivial. % 32.93/33.16 (* end of lemma zenon_L185_ *) % 32.93/33.16 assert (zenon_L186_ : (~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))) -> ((op1 (e13) (e13)) = (e13)) -> False). % 32.93/33.16 do 0 intro. intros zenon_H1d9 zenon_Hfa. % 32.93/33.16 cut (((op1 (e13) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_Hfb]. % 32.93/33.16 cut (((e13) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H123]. % 32.93/33.16 congruence. % 32.93/33.16 apply zenon_H123. apply refl_equal. % 32.93/33.16 exact (zenon_Hfb zenon_Hfa). % 32.93/33.16 (* end of lemma zenon_L186_ *) % 32.93/33.16 assert (zenon_L187_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e11) = (op1 (e13) (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e20) (e20)) = (e22))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> False). % 32.93/33.16 do 0 intro. intros zenon_H1ca zenon_Hd3 zenon_He8 zenon_Hdf zenon_H174 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H2de zenon_H1a0 zenon_H15f zenon_H18a zenon_H186 zenon_Hfd zenon_H311 zenon_H312 zenon_H2ef zenon_H2f7 zenon_H1c3 zenon_H1bf zenon_H90 zenon_H1c4 zenon_H92 zenon_H1b6 zenon_H1a9 zenon_H132 zenon_H11d zenon_H128 zenon_H126 zenon_H12c zenon_H130 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_H93 zenon_Hac zenon_H172 zenon_He4 zenon_H19e zenon_H195 zenon_He9 zenon_H140 zenon_H2e1 zenon_H210 zenon_H1e3 zenon_H20c zenon_H1ec zenon_H209 zenon_H20b zenon_H68 zenon_H5a zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_H30e zenon_H179 zenon_Hf9 zenon_H2f4 zenon_H198 zenon_H168 zenon_H2e9 zenon_H19f zenon_H2e3 zenon_H1dd zenon_H108 zenon_H1a zenon_H2fb zenon_H17 zenon_H2fe zenon_H2fd zenon_Hd7 zenon_He6 zenon_H1e2 zenon_Hb1 zenon_H171 zenon_H16e zenon_H139 zenon_H175 zenon_He5 zenon_H313 zenon_H1cb. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 32.93/33.16 apply (zenon_L46_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 32.93/33.16 apply (zenon_L176_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 32.93/33.16 apply (zenon_L77_); trivial. % 32.93/33.16 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 32.93/33.16 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 32.93/33.16 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.16 apply (zenon_L30_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 32.93/33.16 apply (zenon_L184_); trivial. % 32.93/33.16 apply (zenon_L185_); trivial. % 32.93/33.16 apply (zenon_L181_); trivial. % 32.93/33.16 apply (zenon_L74_); trivial. % 32.93/33.16 apply (zenon_L173_); trivial. % 32.93/33.16 apply (zenon_L27_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 32.93/33.16 apply (zenon_L32_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 32.93/33.16 apply (zenon_L85_); trivial. % 32.93/33.16 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 32.93/33.16 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 32.93/33.16 apply (zenon_L30_); trivial. % 32.93/33.16 apply (zenon_L185_); trivial. % 32.93/33.16 apply (zenon_L74_); trivial. % 32.93/33.16 apply (zenon_L175_); trivial. % 32.93/33.16 apply (zenon_L27_); trivial. % 32.93/33.16 apply (zenon_L186_); trivial. % 32.93/33.16 (* end of lemma zenon_L187_ *) % 32.93/33.16 assert (zenon_L188_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H6f zenon_H38 zenon_H248 zenon_H240 zenon_H31f zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H312 zenon_H2fd zenon_H2fe zenon_H2fb zenon_H108 zenon_H30e zenon_H20b zenon_H1ec zenon_H210 zenon_H140 zenon_H126 zenon_H1bf zenon_H19f zenon_H172 zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H2f7 zenon_H179 zenon_H311 zenon_H313 zenon_H171 zenon_H16e zenon_H174 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H175 zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H1a0 zenon_H18a zenon_H186 zenon_H1cb zenon_H1a9 zenon_H1b6 zenon_H1c4 zenon_H1c3 zenon_H1ca zenon_H71 zenon_H62 zenon_H54 zenon_H4e zenon_H5a zenon_H4a zenon_H40 zenon_H2b8 zenon_H5e zenon_H73 zenon_H2aa zenon_H211 zenon_H27a zenon_H2be zenon_H23a zenon_H2c9 zenon_H2c5 zenon_H209 zenon_H2cd zenon_H251 zenon_H14 zenon_H24b zenon_H2d0 zenon_H234 zenon_H25f zenon_H1e7 zenon_H1dd zenon_H1e3 zenon_H2d1 zenon_H247 zenon_H33 zenon_H70 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H277 zenon_H279. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.00/33.17 apply (zenon_L7_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.00/33.17 apply (zenon_L153_); trivial. % 33.00/33.17 apply (zenon_L187_); trivial. % 33.00/33.17 apply (zenon_L91_); trivial. % 33.00/33.17 apply (zenon_L111_); trivial. % 33.00/33.17 apply (zenon_L8_); trivial. % 33.00/33.17 apply (zenon_L124_); trivial. % 33.00/33.17 apply (zenon_L4_); trivial. % 33.00/33.17 (* end of lemma zenon_L188_ *) % 33.00/33.17 assert (zenon_L189_ : ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H279 zenon_H14 zenon_H277 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H312 zenon_H2fd zenon_H2fe zenon_H2fb zenon_H108 zenon_H1dd zenon_H30e zenon_H5a zenon_H68 zenon_H20b zenon_H209 zenon_H1ec zenon_H1e3 zenon_H210 zenon_H140 zenon_H126 zenon_H1bf zenon_H19f zenon_H172 zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H2f7 zenon_H179 zenon_H311 zenon_H313 zenon_H171 zenon_H16e zenon_H174 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H175 zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H1a0 zenon_H18a zenon_H186 zenon_H1cb zenon_H1a9 zenon_H1b6 zenon_H1c4 zenon_H1c3 zenon_H1ca zenon_H38. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.00/33.17 apply (zenon_L7_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.00/33.17 apply (zenon_L187_); trivial. % 33.00/33.17 apply (zenon_L111_); trivial. % 33.00/33.17 apply (zenon_L124_); trivial. % 33.00/33.17 (* end of lemma zenon_L189_ *) % 33.00/33.17 assert (zenon_L190_ : ((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (((op2 (e21) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/((op2 (e21) (e23)) = (e23))))) -> (~((e20) = (e23))) -> (~((e22) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((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 (e23) (e23)) = (e23)))\/((op2 (e23) (e23)) = (e23))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e20) (e20)) = (e20)))\/((op2 (e20) (e20)) = (e20))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H2a8 zenon_H87 zenon_H70 zenon_H2d1 zenon_H25f zenon_H2d0 zenon_H24b zenon_H251 zenon_H2cd zenon_H2c5 zenon_H2c9 zenon_H2be zenon_H27a zenon_H73 zenon_H5e zenon_H2b8 zenon_H40 zenon_H4a zenon_H4e zenon_H54 zenon_H62 zenon_H71 zenon_H31f zenon_H6f zenon_H33 zenon_H38 zenon_H243 zenon_H23a zenon_H244 zenon_H234 zenon_H239 zenon_H245 zenon_H22c zenon_H21c zenon_H220 zenon_H22e zenon_H1dc zenon_H1dd zenon_H211 zenon_H1ec zenon_H201 zenon_H1fd zenon_H20b zenon_H1e7 zenon_H1e3 zenon_H5a zenon_H209 zenon_H210 zenon_H246 zenon_H247 zenon_H240 zenon_H248 zenon_H19 zenon_H1a zenon_H21 zenon_H28 zenon_H2e zenon_H279 zenon_H277 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H312 zenon_H2fd zenon_H2fe zenon_H2fb zenon_H108 zenon_H30e zenon_H140 zenon_H126 zenon_H1bf zenon_H19f zenon_H172 zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H2f7 zenon_H179 zenon_H311 zenon_H313 zenon_H171 zenon_H16e zenon_H174 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H175 zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H1a0 zenon_H18a zenon_H186 zenon_H1cb zenon_H1a9 zenon_H1b6 zenon_H1c4 zenon_H1c3 zenon_H1ca zenon_H2a5 zenon_H83 zenon_H17. % 33.00/33.17 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.00/33.17 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab. % 33.00/33.17 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H223. zenon_intro zenon_H2ad. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.00/33.17 apply (zenon_L188_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.00/33.17 apply (zenon_L9_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 33.00/33.17 apply (zenon_L112_); trivial. % 33.00/33.17 apply (zenon_L189_); trivial. % 33.00/33.17 apply (zenon_L23_); trivial. % 33.00/33.17 (* end of lemma zenon_L190_ *) % 33.00/33.17 assert (zenon_L191_ : (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> ((op2 (e20) (e22)) = (e22)) -> False). % 33.00/33.17 do 0 intro. intros zenon_H211 zenon_H1e2 zenon_H1e3 zenon_H1a zenon_H1dd zenon_H1e7 zenon_H285 zenon_H206. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 33.00/33.17 exact (zenon_H1e2 zenon_H1de). % 33.00/33.17 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 33.00/33.17 apply (zenon_L90_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 33.00/33.17 apply (zenon_L91_); trivial. % 33.00/33.17 cut (((op2 (e20) (e22)) = (e22)) = ((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))). % 33.00/33.17 intro zenon_D_pnotp. % 33.00/33.17 apply zenon_H285. % 33.00/33.17 rewrite <- zenon_D_pnotp. % 33.00/33.17 exact zenon_H206. % 33.00/33.17 cut (((e22) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1f8]. % 33.00/33.17 cut (((op2 (e20) (e22)) = (op2 (e20) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H287]. % 33.00/33.17 congruence. % 33.00/33.17 elim (classic ((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (op2 (e23) (e20))))); [ zenon_intro zenon_H288 | zenon_intro zenon_H289 ]. % 33.00/33.17 cut (((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (op2 (e23) (e20)))) = ((op2 (e20) (e22)) = (op2 (e20) (op2 (e23) (e20))))). % 33.00/33.17 intro zenon_D_pnotp. % 33.00/33.17 apply zenon_H287. % 33.00/33.17 rewrite <- zenon_D_pnotp. % 33.00/33.17 exact zenon_H288. % 33.00/33.17 cut (((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (op2 (e23) (e20))))); [idtac | apply NNPP; zenon_intro zenon_H289]. % 33.00/33.17 cut (((op2 (e20) (op2 (e23) (e20))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H283]. % 33.00/33.17 congruence. % 33.00/33.17 apply (zenon_L128_); trivial. % 33.00/33.17 apply zenon_H289. apply refl_equal. % 33.00/33.17 apply zenon_H289. apply refl_equal. % 33.00/33.17 apply zenon_H1f8. apply sym_equal. exact zenon_H1f7. % 33.00/33.17 (* end of lemma zenon_L191_ *) % 33.00/33.17 assert (zenon_L192_ : (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> ((op2 (e21) (e23)) = (e23)) -> ((op2 (e23) (e21)) = (e23)) -> False). % 33.00/33.17 do 0 intro. intros zenon_H2b1 zenon_H21f zenon_H236. % 33.00/33.17 cut (((op2 (e21) (e23)) = (e23)) = ((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))). % 33.00/33.17 intro zenon_D_pnotp. % 33.00/33.17 apply zenon_H2b1. % 33.00/33.17 rewrite <- zenon_D_pnotp. % 33.00/33.17 exact zenon_H21f. % 33.00/33.17 cut (((e23) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H237]. % 33.00/33.17 cut (((op2 (e21) (e23)) = (op2 (e21) (op2 (e23) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H320]. % 33.00/33.17 congruence. % 33.00/33.17 elim (classic ((op2 (e21) (op2 (e23) (e21))) = (op2 (e21) (op2 (e23) (e21))))); [ zenon_intro zenon_H321 | zenon_intro zenon_H322 ]. % 33.00/33.17 cut (((op2 (e21) (op2 (e23) (e21))) = (op2 (e21) (op2 (e23) (e21)))) = ((op2 (e21) (e23)) = (op2 (e21) (op2 (e23) (e21))))). % 33.00/33.17 intro zenon_D_pnotp. % 33.00/33.17 apply zenon_H320. % 33.00/33.17 rewrite <- zenon_D_pnotp. % 33.00/33.17 exact zenon_H321. % 33.00/33.17 cut (((op2 (e21) (op2 (e23) (e21))) = (op2 (e21) (op2 (e23) (e21))))); [idtac | apply NNPP; zenon_intro zenon_H322]. % 33.00/33.17 cut (((op2 (e21) (op2 (e23) (e21))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H323]. % 33.00/33.17 congruence. % 33.00/33.17 cut (((op2 (e23) (e21)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H324]. % 33.00/33.17 cut (((e21) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H82]. % 33.00/33.17 congruence. % 33.00/33.17 apply zenon_H82. apply refl_equal. % 33.00/33.17 exact (zenon_H324 zenon_H236). % 33.00/33.17 apply zenon_H322. apply refl_equal. % 33.00/33.17 apply zenon_H322. apply refl_equal. % 33.00/33.17 apply zenon_H237. apply sym_equal. exact zenon_H236. % 33.00/33.17 (* end of lemma zenon_L192_ *) % 33.00/33.17 assert (zenon_L193_ : (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e22)) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> ((op2 (e23) (e21)) = (e23)) -> False). % 33.00/33.17 do 0 intro. intros zenon_H2cd zenon_H2be zenon_H1a zenon_H17 zenon_H23a zenon_H20a zenon_H209 zenon_H2b1 zenon_H236. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2cd); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2ce ]. % 33.00/33.17 apply (zenon_L145_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2ce); [ zenon_intro zenon_H23b | zenon_intro zenon_H2cf ]. % 33.00/33.17 apply (zenon_L110_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H21f ]. % 33.00/33.17 apply (zenon_L100_); trivial. % 33.00/33.17 apply (zenon_L192_); trivial. % 33.00/33.17 (* end of lemma zenon_L193_ *) % 33.00/33.17 assert (zenon_L194_ : ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((op2 (e22) (e21)) = (e22)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H239 zenon_H1e2 zenon_H211 zenon_H69 zenon_H4a zenon_H1e7 zenon_H1a zenon_H1dd zenon_H1e3 zenon_H285 zenon_H2cd zenon_H2b1 zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_H17. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H18 | zenon_intro zenon_H236 ]. % 33.00/33.17 apply zenon_H18. apply sym_equal. exact zenon_H17. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H1de | zenon_intro zenon_H212 ]. % 33.00/33.17 exact (zenon_H1e2 zenon_H1de). % 33.00/33.17 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H213 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 33.00/33.17 exact (zenon_H1e2 zenon_H1de). % 33.00/33.17 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 33.00/33.17 apply (zenon_L90_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 33.00/33.17 apply (zenon_L91_); trivial. % 33.00/33.17 apply (zenon_L146_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H206 | zenon_intro zenon_H20a ]. % 33.00/33.17 apply (zenon_L191_); trivial. % 33.00/33.17 apply (zenon_L193_); trivial. % 33.00/33.17 (* end of lemma zenon_L194_ *) % 33.00/33.17 assert (zenon_L195_ : ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> ((op2 (e22) (e23)) = (e22)) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H239 zenon_H1e2 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H1e7 zenon_H2cd zenon_H2b1 zenon_H2c4 zenon_H2c5 zenon_H23a zenon_H2be zenon_H211 zenon_H17. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H18 | zenon_intro zenon_H236 ]. % 33.00/33.17 apply zenon_H18. apply sym_equal. exact zenon_H17. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 33.00/33.17 exact (zenon_H1e2 zenon_H1de). % 33.00/33.17 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 33.00/33.17 apply (zenon_L90_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 33.00/33.17 apply (zenon_L91_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2cd); [ zenon_intro zenon_H2bd | zenon_intro zenon_H2ce ]. % 33.00/33.17 apply (zenon_L145_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2ce); [ zenon_intro zenon_H23b | zenon_intro zenon_H2cf ]. % 33.00/33.17 apply (zenon_L110_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2cf); [ zenon_intro zenon_H1f3 | zenon_intro zenon_H21f ]. % 33.00/33.17 apply (zenon_L148_); trivial. % 33.00/33.17 apply (zenon_L192_); trivial. % 33.00/33.17 (* end of lemma zenon_L195_ *) % 33.00/33.17 assert (zenon_L196_ : (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (e22))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H2c9 zenon_H210 zenon_H209 zenon_H285 zenon_H4a zenon_H27e zenon_H239 zenon_H1e2 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H1e7 zenon_H2cd zenon_H2b1 zenon_H2c5 zenon_H23a zenon_H2be zenon_H211 zenon_H17. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2c9); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H2ca ]. % 33.00/33.17 apply (zenon_L91_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2ca); [ zenon_intro zenon_H69 | zenon_intro zenon_H2cb ]. % 33.00/33.17 apply (zenon_L194_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2cb); [ zenon_intro zenon_H68 | zenon_intro zenon_H2c4 ]. % 33.00/33.17 exact (zenon_H27e zenon_H68). % 33.00/33.17 apply (zenon_L195_); trivial. % 33.00/33.17 (* end of lemma zenon_L196_ *) % 33.00/33.17 assert (zenon_L197_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e13)) = (e12)) -> False). % 33.00/33.17 do 0 intro. intros zenon_H15f zenon_H93 zenon_H126 zenon_H140 zenon_H13a zenon_H145 zenon_Hdd zenon_H198 zenon_H199. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H141 | zenon_intro zenon_H162 ]. % 33.00/33.17 apply (zenon_L57_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H13f | zenon_intro zenon_H163 ]. % 33.00/33.17 exact (zenon_H13a zenon_H13f). % 33.00/33.17 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H144 | zenon_intro zenon_H151 ]. % 33.00/33.17 apply (zenon_L58_); trivial. % 33.00/33.17 apply (zenon_L75_); trivial. % 33.00/33.17 (* end of lemma zenon_L197_ *) % 33.00/33.17 assert (zenon_L198_ : ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> (~((op1 (e10) (e10)) = (e12))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H171 zenon_Had zenon_H16e zenon_H1e2 zenon_H30e zenon_H145 zenon_Hdd zenon_H198 zenon_H15f zenon_H140 zenon_H126 zenon_H93 zenon_H1bf zenon_H1d6 zenon_H2e1 zenon_H1dd zenon_H108 zenon_H1a zenon_H2fb zenon_H17 zenon_H2fe zenon_H2fd zenon_H2e2 zenon_H211 zenon_H285 zenon_H1e7 zenon_H1e3 zenon_H2cd zenon_H236 zenon_H2b1 zenon_H209 zenon_H23a zenon_H2be zenon_H210. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H1de | zenon_intro zenon_H212 ]. % 33.00/33.17 exact (zenon_H1e2 zenon_H1de). % 33.00/33.17 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H213 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H30e); [ zenon_intro zenon_H2e5 | zenon_intro zenon_H30f ]. % 33.00/33.17 exact (zenon_H2e2 zenon_H2e5). % 33.00/33.17 apply (zenon_or_s _ _ zenon_H30f); [ zenon_intro zenon_H2d8 | zenon_intro zenon_H310 ]. % 33.00/33.17 apply (zenon_L167_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H310); [ zenon_intro zenon_H30b | zenon_intro zenon_H199 ]. % 33.00/33.17 apply (zenon_L177_); trivial. % 33.00/33.17 apply (zenon_L197_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H206 | zenon_intro zenon_H20a ]. % 33.00/33.17 apply (zenon_L191_); trivial. % 33.00/33.17 apply (zenon_L193_); trivial. % 33.00/33.17 apply (zenon_L65_); trivial. % 33.00/33.17 (* end of lemma zenon_L198_ *) % 33.00/33.17 assert (zenon_L199_ : ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H239 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H312 zenon_H1e2 zenon_H2fd zenon_H2fe zenon_H2fb zenon_H1a zenon_H108 zenon_H1dd zenon_H30e zenon_H5a zenon_H68 zenon_H20b zenon_H209 zenon_H1ec zenon_H20c zenon_H1e3 zenon_H210 zenon_H140 zenon_H126 zenon_H1bf zenon_H19f zenon_H172 zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H2f7 zenon_H179 zenon_H311 zenon_H313 zenon_H171 zenon_H16e zenon_H174 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H175 zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H1a0 zenon_H18a zenon_H186 zenon_H211 zenon_H285 zenon_H1e7 zenon_H2cd zenon_H2b1 zenon_H23a zenon_H2be zenon_H1ca zenon_H17. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H18 | zenon_intro zenon_H236 ]. % 33.00/33.17 apply zenon_H18. apply sym_equal. exact zenon_H17. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.00/33.17 apply (zenon_L46_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.00/33.17 apply (zenon_L176_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.00/33.17 apply (zenon_L77_); trivial. % 33.00/33.17 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.00/33.17 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.00/33.17 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.00/33.17 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.00/33.17 apply (zenon_L30_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 33.00/33.17 apply (zenon_L184_); trivial. % 33.00/33.17 apply (zenon_L198_); trivial. % 33.00/33.17 apply (zenon_L181_); trivial. % 33.00/33.17 apply (zenon_L74_); trivial. % 33.00/33.17 apply (zenon_L173_); trivial. % 33.00/33.17 apply (zenon_L27_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.00/33.17 apply (zenon_L32_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.00/33.17 apply (zenon_L30_); trivial. % 33.00/33.17 apply (zenon_L198_); trivial. % 33.00/33.17 apply (zenon_L175_); trivial. % 33.00/33.17 apply (zenon_L186_); trivial. % 33.00/33.17 (* end of lemma zenon_L199_ *) % 33.00/33.17 assert (zenon_L200_ : ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H279 zenon_H14 zenon_H277 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_H2c9 zenon_H2c5 zenon_H210 zenon_H2be zenon_H23a zenon_H209 zenon_H2b1 zenon_H2cd zenon_H285 zenon_H1e3 zenon_H4a zenon_H211 zenon_H239 zenon_H1dd zenon_H1e7 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H312 zenon_H2fd zenon_H2fe zenon_H2fb zenon_H108 zenon_H30e zenon_H5a zenon_H20b zenon_H1ec zenon_H140 zenon_H126 zenon_H1bf zenon_H19f zenon_H172 zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H2f7 zenon_H179 zenon_H311 zenon_H313 zenon_H171 zenon_H16e zenon_H174 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H175 zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H1a0 zenon_H18a zenon_H186 zenon_H1ca zenon_H31f zenon_H38. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.00/33.17 apply (zenon_L7_); trivial. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.00/33.17 apply (zenon_L196_); trivial. % 33.00/33.17 apply (zenon_L199_); trivial. % 33.00/33.17 apply (zenon_L111_); trivial. % 33.00/33.17 apply (zenon_L124_); trivial. % 33.00/33.17 (* end of lemma zenon_L200_ *) % 33.00/33.17 assert (zenon_L201_ : ((~((op2 (e20) (e20)) = (e20)))\/((op2 (e20) (e20)) = (e20))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e10) (e11))) = (op2 (h4 (e10)) (h4 (e11))))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((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 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H2a5 zenon_H1ca zenon_H1c3 zenon_H1c4 zenon_H1b6 zenon_H1a9 zenon_H1cb zenon_H186 zenon_H18a zenon_H1a0 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H175 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H174 zenon_H16e zenon_H171 zenon_H313 zenon_H311 zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H30e zenon_H108 zenon_H2fb zenon_H2fe zenon_H2fd zenon_H312 zenon_H195 zenon_H19e zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H277 zenon_H38 zenon_H247 zenon_H245 zenon_H29f zenon_H29e zenon_H285 zenon_H28b zenon_H293 zenon_H297 zenon_H239 zenon_H234 zenon_H244 zenon_H1dc zenon_H1dd zenon_H211 zenon_H1ec zenon_H68 zenon_H201 zenon_H1fd zenon_H20b zenon_H1e7 zenon_H1e3 zenon_H5a zenon_H209 zenon_H210 zenon_H240 zenon_H248 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H279. % 33.00/33.17 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 33.00/33.17 apply (zenon_L138_); trivial. % 33.00/33.17 apply (zenon_L189_); trivial. % 33.00/33.17 (* end of lemma zenon_L201_ *) % 33.00/33.17 assert (zenon_L202_ : (~((h4 (e12)) = (e22))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> False). % 33.00/33.17 do 0 intro. intros zenon_H325 zenon_H2fe zenon_H1dd. % 33.00/33.17 cut (((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((h4 (e12)) = (e22))). % 33.00/33.17 intro zenon_D_pnotp. % 33.00/33.17 apply zenon_H325. % 33.00/33.17 rewrite <- zenon_D_pnotp. % 33.00/33.17 exact zenon_H2fe. % 33.00/33.17 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H326]. % 33.00/33.17 cut (((h4 (e12)) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H327]. % 33.00/33.17 congruence. % 33.00/33.17 apply zenon_H327. apply refl_equal. % 33.02/33.18 apply zenon_H326. apply sym_equal. exact zenon_H1dd. % 33.02/33.18 (* end of lemma zenon_L202_ *) % 33.02/33.18 assert (zenon_L203_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H71 zenon_H75 zenon_H4e zenon_H55 zenon_H4a zenon_H34 zenon_H40 zenon_H54 zenon_H90 zenon_Hd7 zenon_H328 zenon_H2fb zenon_H108 zenon_H1a zenon_H2fe zenon_H1dd zenon_Hcd zenon_Hb9 zenon_Had zenon_Hc3 zenon_Hce zenon_Hc7 zenon_Hea zenon_He6 zenon_H62 zenon_H17. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 33.02/33.18 exact (zenon_H75 zenon_H78). % 33.02/33.18 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H4b | zenon_intro zenon_H79 ]. % 33.02/33.18 apply (zenon_L15_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H59 | zenon_intro zenon_H63 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 33.02/33.18 exact (zenon_Hea zenon_Hed). % 33.02/33.18 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 33.02/33.18 apply (zenon_L38_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 33.02/33.18 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H328. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H2fb. % 33.02/33.18 cut (((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H329]. % 33.02/33.18 cut (((h4 (e11)) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H32a]. % 33.02/33.18 congruence. % 33.02/33.18 elim (classic ((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [ zenon_intro zenon_H32b | zenon_intro zenon_H32c ]. % 33.02/33.18 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12)))) = ((h4 (e11)) = (h4 (op1 (e10) (e12))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H32a. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H32b. % 33.02/33.18 cut (((h4 (op1 (e10) (e12))) = (h4 (op1 (e10) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H32c]. % 33.02/33.18 cut (((h4 (op1 (e10) (e12))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H32d]. % 33.02/33.18 congruence. % 33.02/33.18 cut (((op1 (e10) (e12)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hf7]. % 33.02/33.18 congruence. % 33.02/33.18 exact (zenon_Hf7 zenon_Hef). % 33.02/33.18 apply zenon_H32c. apply refl_equal. % 33.02/33.18 apply zenon_H32c. apply refl_equal. % 33.02/33.18 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H32e | zenon_intro zenon_H32f ]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e23) (e23)) = (op2 (h4 (e10)) (h4 (e12))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H329. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H32e. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H32f]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H330]. % 33.02/33.18 congruence. % 33.02/33.18 cut (((op2 (e20) (e22)) = (e21)) = ((op2 (h4 (e10)) (h4 (e12))) = (op2 (e23) (e23)))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H330. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H59. % 33.02/33.18 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H331]. % 33.02/33.18 cut (((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H332]. % 33.02/33.18 congruence. % 33.02/33.18 elim (classic ((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [ zenon_intro zenon_H32e | zenon_intro zenon_H32f ]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12)))) = ((op2 (e20) (e22)) = (op2 (h4 (e10)) (h4 (e12))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H332. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H32e. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (h4 (e10)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H32f]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e12))) = (op2 (e20) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H333]. % 33.02/33.18 congruence. % 33.02/33.18 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.02/33.18 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 33.02/33.18 congruence. % 33.02/33.18 apply (zenon_L47_); trivial. % 33.02/33.18 apply (zenon_L202_); trivial. % 33.02/33.18 apply zenon_H32f. apply refl_equal. % 33.02/33.18 apply zenon_H32f. apply refl_equal. % 33.02/33.18 exact (zenon_H331 zenon_H17). % 33.02/33.18 apply zenon_H32f. apply refl_equal. % 33.02/33.18 apply zenon_H32f. apply refl_equal. % 33.02/33.18 apply (zenon_L41_); trivial. % 33.02/33.18 apply (zenon_L19_); trivial. % 33.02/33.18 (* end of lemma zenon_L203_ *) % 33.02/33.18 assert (zenon_L204_ : ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> False). % 33.02/33.18 do 0 intro. intros zenon_He4 zenon_Hb1 zenon_H71 zenon_H62 zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_H328 zenon_H2fb zenon_H1dd zenon_H2fe zenon_H1a zenon_H108 zenon_Hd7 zenon_He6 zenon_H40 zenon_H34 zenon_H17 zenon_H4a zenon_H55 zenon_H4e zenon_H54 zenon_H75 zenon_H172 zenon_H1d0 zenon_H2e1 zenon_H2de zenon_H179 zenon_H2e3 zenon_H1bf zenon_H126 zenon_H140 zenon_He9 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_H311 zenon_H104 zenon_H313. % 33.02/33.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.18 apply (zenon_L30_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.02/33.18 apply (zenon_L203_); trivial. % 33.02/33.18 apply (zenon_L159_); trivial. % 33.02/33.18 apply (zenon_L173_); trivial. % 33.02/33.18 apply (zenon_L27_); trivial. % 33.02/33.18 (* end of lemma zenon_L204_ *) % 33.02/33.18 assert (zenon_L205_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((e11) = (e13))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H1ca zenon_Hd3 zenon_He8 zenon_Hdf zenon_H1cb zenon_H311 zenon_H2e3 zenon_H2de zenon_H174 zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_Hf9 zenon_H1a0 zenon_H195 zenon_H15f zenon_H179 zenon_H18a zenon_H186 zenon_H19f zenon_H19e zenon_Hfd zenon_He4 zenon_Hb1 zenon_H71 zenon_H62 zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_H328 zenon_H2fb zenon_H1dd zenon_H2fe zenon_H1a zenon_H108 zenon_Hd7 zenon_He6 zenon_H40 zenon_H34 zenon_H17 zenon_H4a zenon_H55 zenon_H4e zenon_H54 zenon_H75 zenon_H172 zenon_H2e1 zenon_H1bf zenon_H126 zenon_H140 zenon_H2f4 zenon_H198 zenon_H168 zenon_H2e9 zenon_H30e zenon_He9 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_H171 zenon_H16e zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H175 zenon_Hac zenon_He5 zenon_H313. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.02/33.18 apply (zenon_L46_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 33.02/33.18 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.02/33.18 apply (zenon_L204_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.02/33.18 apply (zenon_L32_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.02/33.18 apply (zenon_L66_); trivial. % 33.02/33.18 apply (zenon_L204_); trivial. % 33.02/33.18 apply (zenon_L45_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.02/33.18 apply (zenon_L77_); trivial. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.02/33.18 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.18 apply (zenon_L30_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.02/33.18 apply (zenon_L203_); trivial. % 33.02/33.18 apply (zenon_L181_); trivial. % 33.02/33.18 apply (zenon_L175_); trivial. % 33.02/33.18 apply (zenon_L27_); trivial. % 33.02/33.18 (* end of lemma zenon_L205_ *) % 33.02/33.18 assert (zenon_L206_ : ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20)))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((op2 (e22) (e21)) = (e22)) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H31f zenon_H6a zenon_H71 zenon_H62 zenon_H54 zenon_H4e zenon_H5a zenon_H4a zenon_H17 zenon_H40 zenon_H76 zenon_H2b8 zenon_H1fa zenon_H5e zenon_H73 zenon_H34 zenon_H2aa zenon_H75 zenon_H2d0 zenon_H69 zenon_H2d1. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H2d1); [ zenon_intro zenon_H2b9 | zenon_intro zenon_H2c4 ]. % 33.02/33.18 apply (zenon_L144_); trivial. % 33.02/33.18 apply (zenon_L152_); trivial. % 33.02/33.18 apply (zenon_L20_); trivial. % 33.02/33.18 (* end of lemma zenon_L206_ *) % 33.02/33.18 assert (zenon_L207_ : ((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23))))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H2a8 zenon_H6f zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H70 zenon_H33 zenon_H74 zenon_H2d1 zenon_H2d0 zenon_H73 zenon_H5e zenon_H2b8 zenon_H5a zenon_H6a zenon_H31f zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H71 zenon_H62 zenon_H328 zenon_H2fb zenon_H1dd zenon_H2fe zenon_H108 zenon_H40 zenon_H4a zenon_H4e zenon_H54 zenon_H172 zenon_H2e1 zenon_H2de zenon_H179 zenon_H2e3 zenon_H1bf zenon_H126 zenon_H140 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H195 zenon_H18a zenon_H186 zenon_H19f zenon_H19e zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H1e7 zenon_H247 zenon_H38. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.18 apply (zenon_L7_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H55 | zenon_intro zenon_H69 ]. % 33.02/33.18 apply (zenon_L205_); trivial. % 33.02/33.18 apply (zenon_L206_); trivial. % 33.02/33.18 apply (zenon_L91_); trivial. % 33.02/33.18 apply (zenon_L8_); trivial. % 33.02/33.18 apply (zenon_L4_); trivial. % 33.02/33.18 (* end of lemma zenon_L207_ *) % 33.02/33.18 assert (zenon_L208_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((op2 (e20) (e20)) = (e20)) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H6f zenon_H38 zenon_H1ca zenon_H2f4 zenon_H2e9 zenon_H30e zenon_H19e zenon_H19f zenon_H186 zenon_H18a zenon_H195 zenon_H198 zenon_H1a0 zenon_H171 zenon_H16e zenon_H173 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H174 zenon_H168 zenon_H175 zenon_H1cb zenon_H313 zenon_H311 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H179 zenon_H2de zenon_H2e1 zenon_H172 zenon_H54 zenon_H4e zenon_H4a zenon_H40 zenon_H108 zenon_H2fe zenon_H1dd zenon_H2fb zenon_H328 zenon_H62 zenon_H71 zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H239 zenon_H211 zenon_H1e7 zenon_H1e3 zenon_H285 zenon_H2cd zenon_H2b1 zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_H74 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H277 zenon_H14 zenon_H279. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.18 apply (zenon_L7_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H55 | zenon_intro zenon_H69 ]. % 33.02/33.18 apply (zenon_L205_); trivial. % 33.02/33.18 apply (zenon_L194_); trivial. % 33.02/33.18 apply (zenon_L124_); trivial. % 33.02/33.18 apply (zenon_L4_); trivial. % 33.02/33.18 (* end of lemma zenon_L208_ *) % 33.02/33.18 assert (zenon_L209_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H6f zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H74 zenon_H68 zenon_H6a zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H71 zenon_H62 zenon_H328 zenon_H2fb zenon_H1dd zenon_H2fe zenon_H108 zenon_H40 zenon_H4a zenon_H4e zenon_H54 zenon_H172 zenon_H2e1 zenon_H2de zenon_H179 zenon_H2e3 zenon_H1bf zenon_H126 zenon_H140 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H195 zenon_H18a zenon_H186 zenon_H19f zenon_H19e zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H38. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.18 apply (zenon_L7_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H55 | zenon_intro zenon_H69 ]. % 33.02/33.18 apply (zenon_L205_); trivial. % 33.02/33.18 apply (zenon_L20_); trivial. % 33.02/33.18 apply (zenon_L4_); trivial. % 33.02/33.18 (* end of lemma zenon_L209_ *) % 33.02/33.18 assert (zenon_L210_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((e21) = (e23))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e10) (e12))) = (op2 (h4 (e10)) (h4 (e12))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H2a4 zenon_H247 zenon_H31f zenon_H5a zenon_H2b8 zenon_H5e zenon_H73 zenon_H2d0 zenon_H2d1 zenon_H70 zenon_H83 zenon_H248 zenon_H240 zenon_H24b zenon_H25f zenon_H234 zenon_H251 zenon_H20b zenon_H268 zenon_H274 zenon_H27a zenon_H87 zenon_H279 zenon_H277 zenon_H210 zenon_H2be zenon_H23a zenon_H209 zenon_H2cd zenon_H1e3 zenon_H1e7 zenon_H211 zenon_H239 zenon_H33 zenon_H38 zenon_H1ca zenon_H2f4 zenon_H2e9 zenon_H30e zenon_H19e zenon_H19f zenon_H186 zenon_H18a zenon_H195 zenon_H198 zenon_H1a0 zenon_H171 zenon_H16e zenon_H173 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H174 zenon_H168 zenon_H175 zenon_H1cb zenon_H313 zenon_H311 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H179 zenon_H2de zenon_H2e1 zenon_H172 zenon_H54 zenon_H4e zenon_H4a zenon_H40 zenon_H108 zenon_H2fe zenon_H1dd zenon_H2fb zenon_H328 zenon_H62 zenon_H71 zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H6a zenon_H74 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H6f. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.02/33.18 apply (zenon_L24_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.02/33.18 apply (zenon_L207_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.02/33.18 apply (zenon_L127_); trivial. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.02/33.18 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.02/33.18 apply (zenon_L208_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.02/33.18 apply (zenon_L9_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.02/33.18 apply (zenon_L209_); trivial. % 33.02/33.18 apply (zenon_L139_); trivial. % 33.02/33.18 (* end of lemma zenon_L210_ *) % 33.02/33.18 assert (zenon_L211_ : (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e10)) = (e11))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e20) (e23)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (~((e11) = (e13))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> False). % 33.02/33.18 do 0 intro. intros zenon_He6 zenon_Hea zenon_Hc7 zenon_Hce zenon_Hc3 zenon_Had zenon_Hb9 zenon_Hcd zenon_H334 zenon_H1a zenon_H108 zenon_H21b zenon_H335 zenon_Hf9 zenon_H12d zenon_H179 zenon_H18b zenon_H19f zenon_Hd7 zenon_H90. % 33.02/33.18 apply (zenon_or_s _ _ zenon_He6); [ zenon_intro zenon_Hed | zenon_intro zenon_Hec ]. % 33.02/33.18 exact (zenon_Hea zenon_Hed). % 33.02/33.18 apply (zenon_or_s _ _ zenon_Hec); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hee ]. % 33.02/33.18 apply (zenon_L38_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_Hee); [ zenon_intro zenon_Hef | zenon_intro zenon_Hd8 ]. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H19f); [ zenon_intro zenon_H18d | zenon_intro zenon_H1a4 ]. % 33.02/33.18 exact (zenon_H18b zenon_H18d). % 33.02/33.18 apply (zenon_or_s _ _ zenon_H1a4); [ zenon_intro zenon_H178 | zenon_intro zenon_H1a5 ]. % 33.02/33.18 apply (zenon_L67_); trivial. % 33.02/33.18 apply (zenon_or_s _ _ zenon_H1a5); [ zenon_intro zenon_H17c | zenon_intro zenon_H14d ]. % 33.02/33.18 apply (zenon_L68_); trivial. % 33.02/33.18 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H335. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H334. % 33.02/33.18 cut (((e23) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H336]. % 33.02/33.18 cut (((h4 (e13)) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H337]. % 33.02/33.18 congruence. % 33.02/33.18 elim (classic ((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [ zenon_intro zenon_H338 | zenon_intro zenon_H339 ]. % 33.02/33.18 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13)))) = ((h4 (e13)) = (h4 (op1 (e10) (e13))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H337. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H338. % 33.02/33.18 cut (((h4 (op1 (e10) (e13))) = (h4 (op1 (e10) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H339]. % 33.02/33.18 cut (((h4 (op1 (e10) (e13))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H33a]. % 33.02/33.18 congruence. % 33.02/33.18 cut (((op1 (e10) (e13)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H150]. % 33.02/33.18 congruence. % 33.02/33.18 exact (zenon_H150 zenon_H14d). % 33.02/33.18 apply zenon_H339. apply refl_equal. % 33.02/33.18 apply zenon_H339. apply refl_equal. % 33.02/33.18 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H33b | zenon_intro zenon_H33c ]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((e23) = (op2 (h4 (e10)) (h4 (e13))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H336. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H33b. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H33c]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e13))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H33d]. % 33.02/33.18 congruence. % 33.02/33.18 cut (((op2 (e20) (e23)) = (e23)) = ((op2 (h4 (e10)) (h4 (e13))) = (e23))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H33d. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H21b. % 33.02/33.18 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 33.02/33.18 cut (((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H33e]. % 33.02/33.18 congruence. % 33.02/33.18 elim (classic ((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [ zenon_intro zenon_H33b | zenon_intro zenon_H33c ]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13)))) = ((op2 (e20) (e23)) = (op2 (h4 (e10)) (h4 (e13))))). % 33.02/33.18 intro zenon_D_pnotp. % 33.02/33.18 apply zenon_H33e. % 33.02/33.18 rewrite <- zenon_D_pnotp. % 33.02/33.18 exact zenon_H33b. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (h4 (e10)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H33c]. % 33.02/33.18 cut (((op2 (h4 (e10)) (h4 (e13))) = (op2 (e20) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H33f]. % 33.02/33.18 congruence. % 33.02/33.18 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 33.02/33.18 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 33.02/33.18 congruence. % 33.02/33.18 apply (zenon_L47_); trivial. % 33.02/33.18 exact (zenon_H340 zenon_H334). % 33.02/33.18 apply zenon_H33c. apply refl_equal. % 33.02/33.18 apply zenon_H33c. apply refl_equal. % 33.02/33.18 apply zenon_H1da. apply refl_equal. % 33.02/33.18 apply zenon_H33c. apply refl_equal. % 33.02/33.18 apply zenon_H33c. apply refl_equal. % 33.02/33.18 apply (zenon_L41_); trivial. % 33.02/33.18 (* end of lemma zenon_L211_ *) % 33.02/33.18 assert (zenon_L212_ : ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op1 (e10) (e10)) = (e11))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((e11) = (op1 (e13) (e13))) -> False). % 33.02/33.18 do 0 intro. intros zenon_H172 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H20c zenon_H1ec zenon_H68 zenon_H27a zenon_Hea zenon_Hcd zenon_Hc7 zenon_Hce zenon_Hc3 zenon_Had zenon_Hb9 zenon_H19f zenon_H108 zenon_H334 zenon_H335 zenon_Hf9 zenon_H179 zenon_H18b zenon_Hd7 zenon_He6 zenon_H209 zenon_H17 zenon_H62 zenon_H14 zenon_H24b zenon_H20b zenon_H90. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.02/33.19 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H20d ]. % 33.02/33.19 apply (zenon_L90_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 33.02/33.19 exact (zenon_H20c zenon_H20f). % 33.02/33.19 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f3 ]. % 33.02/33.19 apply (zenon_L92_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H27a); [ zenon_intro zenon_H21a | zenon_intro zenon_H27b ]. % 33.02/33.19 apply (zenon_L113_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H27b); [ zenon_intro zenon_H63 | zenon_intro zenon_H27c ]. % 33.02/33.19 apply (zenon_L19_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H27c); [ zenon_intro zenon_H20a | zenon_intro zenon_H21b ]. % 33.02/33.19 apply (zenon_L100_); trivial. % 33.02/33.19 apply (zenon_L211_); trivial. % 33.02/33.19 (* end of lemma zenon_L212_ *) % 33.02/33.19 assert (zenon_L213_ : ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (e22))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> False). % 33.02/33.19 do 0 intro. intros zenon_He4 zenon_H19e zenon_H104 zenon_H195 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_He9 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H1d0 zenon_H20b zenon_H24b zenon_H14 zenon_H62 zenon_H17 zenon_H209 zenon_He6 zenon_Hd7 zenon_H179 zenon_Hf9 zenon_H335 zenon_H334 zenon_H108 zenon_H19f zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_H27a zenon_H68 zenon_H1ec zenon_H20c zenon_H1a zenon_H1dd zenon_H1e3 zenon_H172 zenon_Hb1 zenon_H311 zenon_H313. % 33.02/33.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.19 apply (zenon_L30_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.02/33.19 apply (zenon_L212_); trivial. % 33.02/33.19 apply (zenon_L159_); trivial. % 33.02/33.19 apply (zenon_L74_); trivial. % 33.02/33.19 apply (zenon_L173_); trivial. % 33.02/33.19 apply (zenon_L27_); trivial. % 33.02/33.19 (* end of lemma zenon_L213_ *) % 33.02/33.19 assert (zenon_L214_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H1ca zenon_Hd3 zenon_He8 zenon_Hdf zenon_H2de zenon_H2e3 zenon_He5 zenon_H175 zenon_H174 zenon_H139 zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H1a0 zenon_H15f zenon_H18a zenon_H186 zenon_H16e zenon_H171 zenon_Hfd zenon_H1cb zenon_H313 zenon_H311 zenon_Hb1 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H20c zenon_H1ec zenon_H68 zenon_H27a zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_H19f zenon_H108 zenon_H334 zenon_H335 zenon_Hf9 zenon_H179 zenon_Hd7 zenon_He6 zenon_H209 zenon_H17 zenon_H62 zenon_H14 zenon_H24b zenon_H20b zenon_H2e1 zenon_H140 zenon_H2f4 zenon_H198 zenon_H168 zenon_H2e9 zenon_H30e zenon_He9 zenon_H195 zenon_H19e zenon_He4 zenon_H172 zenon_Hac zenon_H93 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H130 zenon_H12c zenon_H126 zenon_H128 zenon_H11d zenon_H132 zenon_H1a9 zenon_H1b6 zenon_H92 zenon_H1c4 zenon_H90 zenon_H1bf zenon_H1c3. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.02/33.19 apply (zenon_L46_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.02/33.19 apply (zenon_L213_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.02/33.19 apply (zenon_L32_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.02/33.19 apply (zenon_L66_); trivial. % 33.02/33.19 apply (zenon_L213_); trivial. % 33.02/33.19 apply (zenon_L45_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.02/33.19 apply (zenon_L77_); trivial. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.02/33.19 apply (zenon_L85_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.19 apply (zenon_L30_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.02/33.19 apply (zenon_L212_); trivial. % 33.02/33.19 apply (zenon_L181_); trivial. % 33.02/33.19 apply (zenon_L74_); trivial. % 33.02/33.19 apply (zenon_L173_); trivial. % 33.02/33.19 apply (zenon_L27_); trivial. % 33.02/33.19 (* end of lemma zenon_L214_ *) % 33.02/33.19 assert (zenon_L215_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H6f zenon_H38 zenon_H248 zenon_H240 zenon_H31f zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H20b zenon_H179 zenon_H335 zenon_H334 zenon_H108 zenon_H19f zenon_H1ec zenon_H172 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H18a zenon_H186 zenon_H1c3 zenon_H1c4 zenon_H1b6 zenon_H1a9 zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H71 zenon_H62 zenon_H54 zenon_H4e zenon_H5a zenon_H4a zenon_H40 zenon_H2b8 zenon_H5e zenon_H73 zenon_H2aa zenon_H211 zenon_H27a zenon_H2be zenon_H23a zenon_H2c9 zenon_H2c5 zenon_H209 zenon_H2cd zenon_H251 zenon_H14 zenon_H24b zenon_H2d0 zenon_H234 zenon_H25f zenon_H1e7 zenon_H1dd zenon_H1e3 zenon_H2d1 zenon_H247 zenon_H33 zenon_H70 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H277 zenon_H279. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.19 apply (zenon_L7_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.02/33.19 apply (zenon_L153_); trivial. % 33.02/33.19 apply (zenon_L214_); trivial. % 33.02/33.19 apply (zenon_L91_); trivial. % 33.02/33.19 apply (zenon_L111_); trivial. % 33.02/33.19 apply (zenon_L8_); trivial. % 33.02/33.19 apply (zenon_L124_); trivial. % 33.02/33.19 apply (zenon_L4_); trivial. % 33.02/33.19 (* end of lemma zenon_L215_ *) % 33.02/33.19 assert (zenon_L216_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H38 zenon_H1ca zenon_H2f4 zenon_H2e9 zenon_H30e zenon_H1a9 zenon_H1b6 zenon_H1c4 zenon_H1c3 zenon_H186 zenon_H18a zenon_H198 zenon_H1a0 zenon_H171 zenon_H16e zenon_H173 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H174 zenon_H168 zenon_H175 zenon_H1cb zenon_H313 zenon_H311 zenon_H172 zenon_H1e3 zenon_H1dd zenon_H1ec zenon_H68 zenon_H27a zenon_H19f zenon_H108 zenon_H334 zenon_H335 zenon_H179 zenon_H209 zenon_H62 zenon_H14 zenon_H24b zenon_H20b zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H1bf zenon_H126 zenon_H140 zenon_H195 zenon_H19e zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H240 zenon_H248 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.19 apply (zenon_L7_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.02/33.19 apply (zenon_L214_); trivial. % 33.02/33.19 apply (zenon_L111_); trivial. % 33.02/33.19 (* end of lemma zenon_L216_ *) % 33.02/33.19 assert (zenon_L217_ : ((~((op2 (e20) (e20)) = (e20)))\/((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e23) (e23)) = (e23)))\/((op2 (e23) (e23)) = (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> (~((e21) = (e23))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22)))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (((op2 (e21) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/((op2 (e21) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H2a5 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H24b zenon_H62 zenon_H179 zenon_H335 zenon_H334 zenon_H108 zenon_H19f zenon_H27a zenon_H172 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H18a zenon_H186 zenon_H1c3 zenon_H1c4 zenon_H1b6 zenon_H1a9 zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_H247 zenon_H246 zenon_H210 zenon_H209 zenon_H5a zenon_H1e3 zenon_H1e7 zenon_H20b zenon_H1fd zenon_H201 zenon_H68 zenon_H1ec zenon_H211 zenon_H1dd zenon_H1dc zenon_H83 zenon_H22e zenon_H223 zenon_H220 zenon_H21c zenon_H22c zenon_H245 zenon_H239 zenon_H234 zenon_H244 zenon_H23a zenon_H243 zenon_H38. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 33.02/33.19 apply (zenon_L112_); trivial. % 33.02/33.19 apply (zenon_L216_); trivial. % 33.02/33.19 (* end of lemma zenon_L217_ *) % 33.02/33.19 assert (zenon_L218_ : ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H279 zenon_H277 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_H2c9 zenon_H2c5 zenon_H210 zenon_H2be zenon_H23a zenon_H209 zenon_H2b1 zenon_H2cd zenon_H285 zenon_H1e3 zenon_H4a zenon_H211 zenon_H239 zenon_H1dd zenon_H1e7 zenon_H1ca zenon_H2f4 zenon_H2e9 zenon_H30e zenon_H1a9 zenon_H1b6 zenon_H1c4 zenon_H1c3 zenon_H186 zenon_H18a zenon_H198 zenon_H1a0 zenon_H171 zenon_H16e zenon_H173 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H174 zenon_H168 zenon_H175 zenon_H1cb zenon_H313 zenon_H311 zenon_H172 zenon_H1ec zenon_H27a zenon_H19f zenon_H108 zenon_H334 zenon_H335 zenon_H179 zenon_H62 zenon_H14 zenon_H24b zenon_H20b zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H1bf zenon_H126 zenon_H140 zenon_H195 zenon_H19e zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H31f zenon_H38. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.19 apply (zenon_L7_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.02/33.19 apply (zenon_L196_); trivial. % 33.02/33.19 apply (zenon_L214_); trivial. % 33.02/33.19 apply (zenon_L111_); trivial. % 33.02/33.19 apply (zenon_L124_); trivial. % 33.02/33.19 (* end of lemma zenon_L218_ *) % 33.02/33.19 assert (zenon_L219_ : ((~((op2 (e20) (e20)) = (e20)))\/((op2 (e20) (e20)) = (e20))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((h4 (op1 (e10) (e13))) = (op2 (h4 (e10)) (h4 (e13))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (~((op2 (e20) (e23)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((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 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H2a5 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H24b zenon_H62 zenon_H179 zenon_H335 zenon_H334 zenon_H108 zenon_H19f zenon_H27a zenon_H172 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H18a zenon_H186 zenon_H1c3 zenon_H1c4 zenon_H1b6 zenon_H1a9 zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H38 zenon_H247 zenon_H245 zenon_H29f zenon_H29e zenon_H285 zenon_H28b zenon_H293 zenon_H297 zenon_H239 zenon_H234 zenon_H244 zenon_H1dc zenon_H1dd zenon_H211 zenon_H1ec zenon_H68 zenon_H201 zenon_H1fd zenon_H20b zenon_H1e7 zenon_H1e3 zenon_H5a zenon_H209 zenon_H210 zenon_H240 zenon_H248 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H279. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 33.02/33.19 apply (zenon_L138_); trivial. % 33.02/33.19 apply (zenon_L216_); trivial. % 33.02/33.19 (* end of lemma zenon_L219_ *) % 33.02/33.19 assert (zenon_L220_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H38 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_H341 zenon_H108 zenon_H2fb zenon_Hb1 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.19 apply (zenon_L7_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.19 apply (zenon_L30_); trivial. % 33.02/33.19 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e11) (e10))) = (op2 (h4 (e11)) (h4 (e10))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H341. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H2fb. % 33.02/33.19 cut (((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H342]. % 33.02/33.19 cut (((h4 (e11)) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H343]. % 33.02/33.19 congruence. % 33.02/33.19 elim (classic ((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [ zenon_intro zenon_H344 | zenon_intro zenon_H345 ]. % 33.02/33.19 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10)))) = ((h4 (e11)) = (h4 (op1 (e11) (e10))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H343. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H344. % 33.02/33.19 cut (((h4 (op1 (e11) (e10))) = (h4 (op1 (e11) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H345]. % 33.02/33.19 cut (((h4 (op1 (e11) (e10))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H346]. % 33.02/33.19 congruence. % 33.02/33.19 cut (((op1 (e11) (e10)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_Hb7]. % 33.02/33.19 congruence. % 33.02/33.19 exact (zenon_Hb7 zenon_Had). % 33.02/33.19 apply zenon_H345. apply refl_equal. % 33.02/33.19 apply zenon_H345. apply refl_equal. % 33.02/33.19 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H347 | zenon_intro zenon_H348 ]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e23) (e23)) = (op2 (h4 (e11)) (h4 (e10))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H342. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H347. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H349]. % 33.02/33.19 congruence. % 33.02/33.19 cut (((op2 (e21) (e20)) = (e21)) = ((op2 (h4 (e11)) (h4 (e10))) = (op2 (e23) (e23)))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H349. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H34. % 33.02/33.19 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H331]. % 33.02/33.19 cut (((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H34a]. % 33.02/33.19 congruence. % 33.02/33.19 elim (classic ((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [ zenon_intro zenon_H347 | zenon_intro zenon_H348 ]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10)))) = ((op2 (e21) (e20)) = (op2 (h4 (e11)) (h4 (e10))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H34a. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H347. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (h4 (e11)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H348]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e10))) = (op2 (e21) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H34b]. % 33.02/33.19 congruence. % 33.02/33.19 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 33.02/33.19 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 33.02/33.19 congruence. % 33.02/33.19 apply (zenon_L166_); trivial. % 33.02/33.19 apply (zenon_L47_); trivial. % 33.02/33.19 apply zenon_H348. apply refl_equal. % 33.02/33.19 apply zenon_H348. apply refl_equal. % 33.02/33.19 exact (zenon_H331 zenon_H17). % 33.02/33.19 apply zenon_H348. apply refl_equal. % 33.02/33.19 apply zenon_H348. apply refl_equal. % 33.02/33.19 (* end of lemma zenon_L220_ *) % 33.02/33.19 assert (zenon_L221_ : (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op1 (e11) (e11)) = (e10)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H34c zenon_H108 zenon_Hab zenon_H2fb. % 33.02/33.19 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H34c. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H108. % 33.02/33.19 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e11)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H34d]. % 33.02/33.19 cut (((h4 (e10)) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H34e]. % 33.02/33.19 congruence. % 33.02/33.19 elim (classic ((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [ zenon_intro zenon_H34f | zenon_intro zenon_H350 ]. % 33.02/33.19 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11)))) = ((h4 (e10)) = (h4 (op1 (e11) (e11))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H34e. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H34f. % 33.02/33.19 cut (((h4 (op1 (e11) (e11))) = (h4 (op1 (e11) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H350]. % 33.02/33.19 cut (((h4 (op1 (e11) (e11))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H351]. % 33.02/33.19 congruence. % 33.02/33.19 cut (((op1 (e11) (e11)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_Ha8]. % 33.02/33.19 congruence. % 33.02/33.19 exact (zenon_Ha8 zenon_Hab). % 33.02/33.19 apply zenon_H350. apply refl_equal. % 33.02/33.19 apply zenon_H350. apply refl_equal. % 33.02/33.19 cut (((op2 (e23) (e23)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H352]. % 33.02/33.19 cut (((op2 (e23) (e23)) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H352]. % 33.02/33.19 congruence. % 33.02/33.19 apply zenon_H352. apply sym_equal. exact zenon_H2fb. % 33.02/33.19 apply zenon_H352. apply sym_equal. exact zenon_H2fb. % 33.02/33.19 (* end of lemma zenon_L221_ *) % 33.02/33.19 assert (zenon_L222_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((h4 (op1 (e11) (e11))) = (op2 (h4 (e11)) (h4 (e11))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 33.02/33.19 do 0 intro. intros zenon_Ha7 zenon_H92 zenon_H2fb zenon_H108 zenon_H34c zenon_H9a zenon_H93 zenon_H90 zenon_Ha1. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H94 | zenon_intro zenon_Ha9 ]. % 33.02/33.19 apply (zenon_L27_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 33.02/33.19 apply (zenon_L221_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H99 | zenon_intro zenon_Ha0 ]. % 33.02/33.19 apply (zenon_L28_); trivial. % 33.02/33.19 apply (zenon_L29_); trivial. % 33.02/33.19 (* end of lemma zenon_L222_ *) % 33.02/33.19 assert (zenon_L223_ : (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (e13))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((op2 (e21) (e22)) = (e23)) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((e12) = (e13))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H15f zenon_H93 zenon_H126 zenon_H140 zenon_H13a zenon_H145 zenon_Hdd zenon_H160 zenon_Hf9 zenon_Had zenon_H13b zenon_H1dd zenon_H2fe zenon_H17 zenon_H2fb zenon_H225 zenon_H334 zenon_H353 zenon_H153. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H141 | zenon_intro zenon_H162 ]. % 33.02/33.19 apply (zenon_L57_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H13f | zenon_intro zenon_H163 ]. % 33.02/33.19 exact (zenon_H13a zenon_H13f). % 33.02/33.19 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H144 | zenon_intro zenon_H151 ]. % 33.02/33.19 apply (zenon_L58_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H160); [ zenon_intro zenon_H148 | zenon_intro zenon_H164 ]. % 33.02/33.19 apply (zenon_L59_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H164); [ zenon_intro zenon_H13e | zenon_intro zenon_H165 ]. % 33.02/33.19 exact (zenon_H13b zenon_H13e). % 33.02/33.19 apply (zenon_or_s _ _ zenon_H165); [ zenon_intro zenon_H158 | zenon_intro zenon_H152 ]. % 33.02/33.19 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H353. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H334. % 33.02/33.19 cut (((e23) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H354]. % 33.02/33.19 cut (((h4 (e13)) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H355]. % 33.02/33.19 congruence. % 33.02/33.19 elim (classic ((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [ zenon_intro zenon_H356 | zenon_intro zenon_H357 ]. % 33.02/33.19 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12)))) = ((h4 (e13)) = (h4 (op1 (e11) (e12))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H355. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H356. % 33.02/33.19 cut (((h4 (op1 (e11) (e12))) = (h4 (op1 (e11) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H357]. % 33.02/33.19 cut (((h4 (op1 (e11) (e12))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H358]. % 33.02/33.19 congruence. % 33.02/33.19 cut (((op1 (e11) (e12)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H15e]. % 33.02/33.19 congruence. % 33.02/33.19 exact (zenon_H15e zenon_H158). % 33.02/33.19 apply zenon_H357. apply refl_equal. % 33.02/33.19 apply zenon_H357. apply refl_equal. % 33.02/33.19 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H359 | zenon_intro zenon_H35a ]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((e23) = (op2 (h4 (e11)) (h4 (e12))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H354. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H359. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H35a]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e12))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H35b]. % 33.02/33.19 congruence. % 33.02/33.19 cut (((op2 (e21) (e22)) = (e23)) = ((op2 (h4 (e11)) (h4 (e12))) = (e23))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H35b. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H225. % 33.02/33.19 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 33.02/33.19 cut (((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H35c]. % 33.02/33.19 congruence. % 33.02/33.19 elim (classic ((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [ zenon_intro zenon_H359 | zenon_intro zenon_H35a ]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12)))) = ((op2 (e21) (e22)) = (op2 (h4 (e11)) (h4 (e12))))). % 33.02/33.19 intro zenon_D_pnotp. % 33.02/33.19 apply zenon_H35c. % 33.02/33.19 rewrite <- zenon_D_pnotp. % 33.02/33.19 exact zenon_H359. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (h4 (e11)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H35a]. % 33.02/33.19 cut (((op2 (h4 (e11)) (h4 (e12))) = (op2 (e21) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H35d]. % 33.02/33.19 congruence. % 33.02/33.19 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.02/33.19 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 33.02/33.19 congruence. % 33.02/33.19 apply (zenon_L166_); trivial. % 33.02/33.19 apply (zenon_L202_); trivial. % 33.02/33.19 apply zenon_H35a. apply refl_equal. % 33.02/33.19 apply zenon_H35a. apply refl_equal. % 33.02/33.19 apply zenon_H1da. apply refl_equal. % 33.02/33.19 apply zenon_H35a. apply refl_equal. % 33.02/33.19 apply zenon_H35a. apply refl_equal. % 33.02/33.19 apply (zenon_L61_); trivial. % 33.02/33.19 (* end of lemma zenon_L223_ *) % 33.02/33.19 assert (zenon_L224_ : (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e11)) = (e13))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((e12) = (e13))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H35e zenon_H28b zenon_H1a zenon_H34 zenon_H240 zenon_H1ec zenon_H68 zenon_H15f zenon_H93 zenon_H126 zenon_H140 zenon_H13a zenon_H145 zenon_Hdd zenon_H160 zenon_Hf9 zenon_Had zenon_H13b zenon_H1dd zenon_H2fe zenon_H17 zenon_H2fb zenon_H334 zenon_H353 zenon_H153. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H35e); [ zenon_intro zenon_H28a | zenon_intro zenon_H35f ]. % 33.02/33.19 apply (zenon_L131_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H35f); [ zenon_intro zenon_H241 | zenon_intro zenon_H360 ]. % 33.02/33.19 apply (zenon_L111_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H360); [ zenon_intro zenon_H1eb | zenon_intro zenon_H225 ]. % 33.02/33.19 apply (zenon_L92_); trivial. % 33.02/33.19 apply (zenon_L223_); trivial. % 33.02/33.19 (* end of lemma zenon_L224_ *) % 33.02/33.19 assert (zenon_L225_ : ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((e11) = (e13))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> ((op1 (e12) (e12)) = (e12)) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> False). % 33.02/33.19 do 0 intro. intros zenon_Hb1 zenon_H175 zenon_H168 zenon_H28b zenon_H1a zenon_H17 zenon_H240 zenon_H34 zenon_H1ec zenon_H68 zenon_H15f zenon_Hf9 zenon_H353 zenon_H334 zenon_H1dd zenon_H2fe zenon_H2fb zenon_H153 zenon_H160 zenon_Hdd zenon_H145 zenon_H126 zenon_H140 zenon_H35e zenon_H16e zenon_H171 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.19 apply (zenon_L30_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H13b | zenon_intro zenon_H169 ]. % 33.02/33.19 apply (zenon_L224_); trivial. % 33.02/33.19 apply (zenon_L64_); trivial. % 33.02/33.19 apply (zenon_L65_); trivial. % 33.02/33.19 (* end of lemma zenon_L225_ *) % 33.02/33.19 assert (zenon_L226_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (~((e11) = (e13))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H1ca zenon_Hd3 zenon_He8 zenon_Hdf zenon_H2de zenon_H2e3 zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_He5 zenon_H1a0 zenon_H18a zenon_H186 zenon_Hfd zenon_H313 zenon_H311 zenon_H312 zenon_H1bf zenon_H172 zenon_H2e1 zenon_Hc3 zenon_H2f4 zenon_H198 zenon_H2e9 zenon_H30e zenon_Hcd zenon_Hc7 zenon_Hb9 zenon_H179 zenon_H2ef zenon_H19f zenon_Hd7 zenon_He6 zenon_H2f7 zenon_He9 zenon_H195 zenon_H19e zenon_He4 zenon_Hac zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_H171 zenon_H16e zenon_H35e zenon_H140 zenon_H126 zenon_H145 zenon_H160 zenon_H153 zenon_H2fb zenon_H2fe zenon_H1dd zenon_H334 zenon_H353 zenon_Hf9 zenon_H15f zenon_H68 zenon_H1ec zenon_H34 zenon_H240 zenon_H17 zenon_H1a zenon_H28b zenon_H168 zenon_H175 zenon_Hb1. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.02/33.19 apply (zenon_L46_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.19 apply (zenon_L30_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H13b | zenon_intro zenon_H169 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 33.02/33.19 apply (zenon_L165_); trivial. % 33.02/33.19 apply (zenon_L224_); trivial. % 33.02/33.19 apply (zenon_L64_); trivial. % 33.02/33.19 apply (zenon_L65_); trivial. % 33.02/33.19 apply (zenon_L74_); trivial. % 33.02/33.19 apply (zenon_L175_); trivial. % 33.02/33.19 apply (zenon_L27_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.02/33.19 apply (zenon_L32_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.02/33.19 apply (zenon_L225_); trivial. % 33.02/33.19 apply (zenon_L45_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.02/33.19 apply (zenon_L77_); trivial. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.19 apply (zenon_L30_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H175); [ zenon_intro zenon_H13b | zenon_intro zenon_H169 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 33.02/33.19 apply (zenon_L184_); trivial. % 33.02/33.19 apply (zenon_L224_); trivial. % 33.02/33.19 apply (zenon_L181_); trivial. % 33.02/33.19 apply (zenon_L64_); trivial. % 33.02/33.19 apply (zenon_L65_); trivial. % 33.02/33.19 apply (zenon_L74_); trivial. % 33.02/33.19 apply (zenon_L173_); trivial. % 33.02/33.19 apply (zenon_L27_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.02/33.19 apply (zenon_L32_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.02/33.19 apply (zenon_L225_); trivial. % 33.02/33.19 apply (zenon_L186_); trivial. % 33.02/33.19 (* end of lemma zenon_L226_ *) % 33.02/33.19 assert (zenon_L227_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((e12) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H38 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H171 zenon_H16e zenon_H312 zenon_H28b zenon_H240 zenon_H1ec zenon_H68 zenon_H15f zenon_H353 zenon_H334 zenon_H1dd zenon_H2fe zenon_H2fb zenon_H153 zenon_H160 zenon_H145 zenon_H35e zenon_H140 zenon_H126 zenon_H1bf zenon_H19f zenon_H172 zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H2f7 zenon_H179 zenon_H175 zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H313 zenon_H1a0 zenon_H18a zenon_H186 zenon_H30e zenon_H311 zenon_H1ca zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.19 apply (zenon_L7_); trivial. % 33.02/33.19 apply (zenon_L226_); trivial. % 33.02/33.19 (* end of lemma zenon_L227_ *) % 33.02/33.19 assert (zenon_L228_ : ((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H2a8 zenon_H87 zenon_H279 zenon_H277 zenon_H70 zenon_H247 zenon_H2d1 zenon_H1e3 zenon_H1e7 zenon_H25f zenon_H234 zenon_H2d0 zenon_H24b zenon_H251 zenon_H2cd zenon_H209 zenon_H2c5 zenon_H2c9 zenon_H23a zenon_H2be zenon_H27a zenon_H211 zenon_H73 zenon_H5e zenon_H2b8 zenon_H40 zenon_H4a zenon_H5a zenon_H4e zenon_H54 zenon_H62 zenon_H71 zenon_H31f zenon_H248 zenon_H6f zenon_H33 zenon_H2e zenon_H28 zenon_H21 zenon_H1a zenon_H19 zenon_H1ca zenon_H311 zenon_H30e zenon_H186 zenon_H18a zenon_H1a0 zenon_H313 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H175 zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H35e zenon_H145 zenon_H160 zenon_H153 zenon_H2fb zenon_H2fe zenon_H1dd zenon_H334 zenon_H353 zenon_H15f zenon_H1ec zenon_H240 zenon_H28b zenon_H312 zenon_H16e zenon_H171 zenon_H195 zenon_H19e zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H38 zenon_H83 zenon_H17. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.19 apply (zenon_L7_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.02/33.19 apply (zenon_L153_); trivial. % 33.02/33.19 apply (zenon_L226_); trivial. % 33.02/33.19 apply (zenon_L91_); trivial. % 33.02/33.19 apply (zenon_L111_); trivial. % 33.02/33.19 apply (zenon_L8_); trivial. % 33.02/33.19 apply (zenon_L124_); trivial. % 33.02/33.19 apply (zenon_L4_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.02/33.19 apply (zenon_L9_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.02/33.19 apply (zenon_L227_); trivial. % 33.02/33.19 apply (zenon_L23_); trivial. % 33.02/33.19 (* end of lemma zenon_L228_ *) % 33.02/33.19 assert (zenon_L229_ : ((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H2ae zenon_H87 zenon_H2c9 zenon_H2c5 zenon_H210 zenon_H2be zenon_H23a zenon_H209 zenon_H2cd zenon_H1e3 zenon_H4a zenon_H211 zenon_H239 zenon_H1e7 zenon_H31f zenon_H277 zenon_H279 zenon_H33 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H1ca zenon_H311 zenon_H30e zenon_H186 zenon_H18a zenon_H1a0 zenon_H313 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H175 zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H35e zenon_H145 zenon_H160 zenon_H153 zenon_H2fb zenon_H2fe zenon_H1dd zenon_H334 zenon_H353 zenon_H15f zenon_H1ec zenon_H240 zenon_H28b zenon_H312 zenon_H16e zenon_H171 zenon_H195 zenon_H19e zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H38. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.02/33.19 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.19 apply (zenon_L7_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.02/33.19 apply (zenon_L196_); trivial. % 33.02/33.19 apply (zenon_L226_); trivial. % 33.02/33.19 apply (zenon_L124_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.02/33.19 apply (zenon_L9_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.02/33.19 apply (zenon_L227_); trivial. % 33.02/33.19 apply (zenon_L139_); trivial. % 33.02/33.19 (* end of lemma zenon_L229_ *) % 33.02/33.19 assert (zenon_L230_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((e21) = (e23))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e21))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e22)) = (e23))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e12) = (e13))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e11) (e12))) = (op2 (h4 (e11)) (h4 (e12))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.02/33.19 do 0 intro. intros zenon_H2a4 zenon_H6a zenon_H74 zenon_H6f zenon_H71 zenon_H54 zenon_H4e zenon_H5a zenon_H2b8 zenon_H5e zenon_H73 zenon_H2d0 zenon_H2d1 zenon_H247 zenon_H70 zenon_H83 zenon_H248 zenon_H24b zenon_H62 zenon_H25f zenon_H234 zenon_H251 zenon_H20b zenon_H268 zenon_H40 zenon_H274 zenon_H27a zenon_H87 zenon_H2c9 zenon_H2c5 zenon_H210 zenon_H2be zenon_H23a zenon_H209 zenon_H2cd zenon_H1e3 zenon_H4a zenon_H211 zenon_H239 zenon_H1e7 zenon_H31f zenon_H277 zenon_H279 zenon_H33 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H1ca zenon_H311 zenon_H30e zenon_H186 zenon_H18a zenon_H1a0 zenon_H313 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H175 zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H35e zenon_H145 zenon_H160 zenon_H153 zenon_H2fb zenon_H2fe zenon_H1dd zenon_H334 zenon_H353 zenon_H15f zenon_H1ec zenon_H240 zenon_H28b zenon_H312 zenon_H16e zenon_H171 zenon_H195 zenon_H19e zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H38. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.02/33.19 apply (zenon_L24_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.02/33.19 apply (zenon_L228_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.02/33.19 apply (zenon_L127_); trivial. % 33.02/33.19 apply (zenon_L229_); trivial. % 33.02/33.19 (* end of lemma zenon_L230_ *) % 33.02/33.19 assert (zenon_L231_ : (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e11)) = (e12))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> False). % 33.02/33.19 do 0 intro. intros zenon_H20b zenon_H1a zenon_H1e3 zenon_H20c zenon_H1ec zenon_H68 zenon_H15f zenon_H93 zenon_H126 zenon_H140 zenon_H13a zenon_H145 zenon_Hdd zenon_H361 zenon_H2fe zenon_H1dd zenon_H2fb zenon_H17 zenon_H334. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H20d ]. % 33.02/33.19 apply (zenon_L90_); trivial. % 33.02/33.19 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 33.02/33.19 exact (zenon_H20c zenon_H20f). % 33.02/33.19 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f3 ]. % 33.02/33.20 apply (zenon_L92_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H15f); [ zenon_intro zenon_H141 | zenon_intro zenon_H162 ]. % 33.02/33.20 apply (zenon_L57_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H162); [ zenon_intro zenon_H13f | zenon_intro zenon_H163 ]. % 33.02/33.20 exact (zenon_H13a zenon_H13f). % 33.02/33.20 apply (zenon_or_s _ _ zenon_H163); [ zenon_intro zenon_H144 | zenon_intro zenon_H151 ]. % 33.02/33.20 apply (zenon_L58_); trivial. % 33.02/33.20 cut (((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))). % 33.02/33.20 intro zenon_D_pnotp. % 33.02/33.20 apply zenon_H361. % 33.02/33.20 rewrite <- zenon_D_pnotp. % 33.02/33.20 exact zenon_H2fe. % 33.02/33.20 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H362]. % 33.02/33.20 cut (((h4 (e12)) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H363]. % 33.02/33.20 congruence. % 33.02/33.20 elim (classic ((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [ zenon_intro zenon_H364 | zenon_intro zenon_H365 ]. % 33.02/33.20 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13)))) = ((h4 (e12)) = (h4 (op1 (e11) (e13))))). % 33.02/33.20 intro zenon_D_pnotp. % 33.02/33.20 apply zenon_H363. % 33.02/33.20 rewrite <- zenon_D_pnotp. % 33.02/33.20 exact zenon_H364. % 33.02/33.20 cut (((h4 (op1 (e11) (e13))) = (h4 (op1 (e11) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H365]. % 33.02/33.20 cut (((h4 (op1 (e11) (e13))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H366]. % 33.02/33.20 congruence. % 33.02/33.20 cut (((op1 (e11) (e13)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H367]. % 33.02/33.20 congruence. % 33.02/33.20 exact (zenon_H367 zenon_H151). % 33.02/33.20 apply zenon_H365. apply refl_equal. % 33.02/33.20 apply zenon_H365. apply refl_equal. % 33.02/33.20 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H368 | zenon_intro zenon_H369 ]. % 33.02/33.20 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e11)) (h4 (e13))))). % 33.02/33.20 intro zenon_D_pnotp. % 33.02/33.20 apply zenon_H362. % 33.02/33.20 rewrite <- zenon_D_pnotp. % 33.02/33.20 exact zenon_H368. % 33.02/33.20 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H369]. % 33.02/33.20 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H36a]. % 33.02/33.20 congruence. % 33.02/33.20 cut (((op2 (e21) (e23)) = (e22)) = ((op2 (h4 (e11)) (h4 (e13))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))). % 33.02/33.20 intro zenon_D_pnotp. % 33.02/33.20 apply zenon_H36a. % 33.02/33.20 rewrite <- zenon_D_pnotp. % 33.02/33.20 exact zenon_H1f3. % 33.02/33.20 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 33.02/33.20 cut (((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H36b]. % 33.02/33.20 congruence. % 33.02/33.20 elim (classic ((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [ zenon_intro zenon_H368 | zenon_intro zenon_H369 ]. % 33.02/33.20 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13)))) = ((op2 (e21) (e23)) = (op2 (h4 (e11)) (h4 (e13))))). % 33.02/33.20 intro zenon_D_pnotp. % 33.02/33.20 apply zenon_H36b. % 33.02/33.20 rewrite <- zenon_D_pnotp. % 33.02/33.20 exact zenon_H368. % 33.02/33.20 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (h4 (e11)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H369]. % 33.02/33.20 cut (((op2 (h4 (e11)) (h4 (e13))) = (op2 (e21) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H36c]. % 33.02/33.20 congruence. % 33.02/33.20 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 33.02/33.20 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 33.02/33.20 congruence. % 33.02/33.20 apply (zenon_L166_); trivial. % 33.02/33.20 exact (zenon_H340 zenon_H334). % 33.02/33.20 apply zenon_H369. apply refl_equal. % 33.02/33.20 apply zenon_H369. apply refl_equal. % 33.02/33.20 exact (zenon_H308 zenon_H1dd). % 33.02/33.20 apply zenon_H369. apply refl_equal. % 33.02/33.20 apply zenon_H369. apply refl_equal. % 33.02/33.20 (* end of lemma zenon_L231_ *) % 33.02/33.20 assert (zenon_L232_ : ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((op1 (e12) (e12)) = (e12)) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (e22))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> False). % 33.02/33.20 do 0 intro. intros zenon_Hb1 zenon_H20b zenon_H140 zenon_H126 zenon_H145 zenon_Hdd zenon_H361 zenon_H2fe zenon_H334 zenon_H17 zenon_H2fb zenon_H15f zenon_H68 zenon_H1ec zenon_H20c zenon_H1a zenon_H1dd zenon_H1e3 zenon_H16e zenon_H171 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7. % 33.02/33.20 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.20 apply (zenon_L30_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 33.02/33.20 apply (zenon_L231_); trivial. % 33.02/33.20 apply (zenon_L65_); trivial. % 33.02/33.20 (* end of lemma zenon_L232_ *) % 33.02/33.20 assert (zenon_L233_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> False). % 33.02/33.20 do 0 intro. intros zenon_H1ca zenon_Hd3 zenon_He8 zenon_Hdf zenon_H2e3 zenon_H2de zenon_H311 zenon_H1a0 zenon_H18a zenon_H186 zenon_Hfd zenon_H313 zenon_He5 zenon_H175 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_He9 zenon_H2f7 zenon_He6 zenon_Hd7 zenon_H19f zenon_H2ef zenon_Hf9 zenon_H179 zenon_Hb9 zenon_Hc7 zenon_Hcd zenon_H30e zenon_H2e9 zenon_H168 zenon_H198 zenon_H2f4 zenon_Hc3 zenon_H2e1 zenon_H172 zenon_H1bf zenon_H312 zenon_H195 zenon_H19e zenon_He4 zenon_Hac zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_H171 zenon_H16e zenon_H1e3 zenon_H1dd zenon_H1a zenon_H20c zenon_H1ec zenon_H68 zenon_H15f zenon_H2fb zenon_H17 zenon_H334 zenon_H2fe zenon_H361 zenon_H145 zenon_H126 zenon_H140 zenon_H20b zenon_Hb1. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.02/33.20 apply (zenon_L46_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.02/33.20 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.20 apply (zenon_L30_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 33.02/33.20 apply (zenon_L165_); trivial. % 33.02/33.20 apply (zenon_L231_); trivial. % 33.02/33.20 apply (zenon_L65_); trivial. % 33.02/33.20 apply (zenon_L74_); trivial. % 33.02/33.20 apply (zenon_L173_); trivial. % 33.02/33.20 apply (zenon_L27_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.02/33.20 apply (zenon_L32_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.02/33.20 apply (zenon_L232_); trivial. % 33.02/33.20 apply (zenon_L45_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.02/33.20 apply (zenon_L77_); trivial. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.02/33.20 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.02/33.20 apply (zenon_L30_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H171); [ zenon_intro zenon_H13a | zenon_intro zenon_H16f ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 33.02/33.20 apply (zenon_L184_); trivial. % 33.02/33.20 apply (zenon_L231_); trivial. % 33.02/33.20 apply (zenon_L181_); trivial. % 33.02/33.20 apply (zenon_L65_); trivial. % 33.02/33.20 apply (zenon_L74_); trivial. % 33.02/33.20 apply (zenon_L175_); trivial. % 33.02/33.20 apply (zenon_L27_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.02/33.20 apply (zenon_L32_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.02/33.20 apply (zenon_L232_); trivial. % 33.02/33.20 apply (zenon_L186_); trivial. % 33.02/33.20 (* end of lemma zenon_L233_ *) % 33.02/33.20 assert (zenon_L234_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> False). % 33.02/33.20 do 0 intro. intros zenon_H38 zenon_H1ca zenon_H175 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H30e zenon_H186 zenon_H18a zenon_H1a0 zenon_H313 zenon_H311 zenon_H312 zenon_H1e3 zenon_H1dd zenon_H1ec zenon_H68 zenon_H15f zenon_H2fb zenon_H334 zenon_H2fe zenon_H361 zenon_H145 zenon_H20b zenon_H140 zenon_H126 zenon_H1bf zenon_H19f zenon_H172 zenon_H2e1 zenon_H2de zenon_H2e3 zenon_H2f4 zenon_H198 zenon_H2ef zenon_H168 zenon_H2e9 zenon_H2f7 zenon_H179 zenon_H16e zenon_H171 zenon_H195 zenon_H19e zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H240 zenon_H248 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.20 apply (zenon_L7_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.02/33.20 apply (zenon_L233_); trivial. % 33.02/33.20 apply (zenon_L111_); trivial. % 33.02/33.20 (* end of lemma zenon_L234_ *) % 33.02/33.20 assert (zenon_L235_ : ((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.02/33.20 do 0 intro. intros zenon_H2a8 zenon_H87 zenon_H279 zenon_H277 zenon_H70 zenon_H247 zenon_H2d1 zenon_H1e7 zenon_H25f zenon_H234 zenon_H2d0 zenon_H24b zenon_H251 zenon_H2cd zenon_H209 zenon_H2c5 zenon_H2c9 zenon_H23a zenon_H2be zenon_H27a zenon_H211 zenon_H73 zenon_H5e zenon_H2b8 zenon_H40 zenon_H4a zenon_H5a zenon_H4e zenon_H54 zenon_H62 zenon_H71 zenon_H31f zenon_H6f zenon_H33 zenon_H2e zenon_H28 zenon_H21 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H171 zenon_H16e zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H20b zenon_H145 zenon_H361 zenon_H2fe zenon_H334 zenon_H2fb zenon_H15f zenon_H1ec zenon_H1dd zenon_H1e3 zenon_H312 zenon_H311 zenon_H313 zenon_H1a0 zenon_H18a zenon_H186 zenon_H30e zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H175 zenon_H1ca zenon_H38 zenon_H83 zenon_H17. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.20 apply (zenon_L7_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.02/33.20 apply (zenon_L153_); trivial. % 33.02/33.20 apply (zenon_L233_); trivial. % 33.02/33.20 apply (zenon_L91_); trivial. % 33.02/33.20 apply (zenon_L111_); trivial. % 33.02/33.20 apply (zenon_L8_); trivial. % 33.02/33.20 apply (zenon_L124_); trivial. % 33.02/33.20 apply (zenon_L4_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.02/33.20 apply (zenon_L9_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.02/33.20 apply (zenon_L234_); trivial. % 33.02/33.20 apply (zenon_L23_); trivial. % 33.02/33.20 (* end of lemma zenon_L235_ *) % 33.02/33.20 assert (zenon_L236_ : ((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.02/33.20 do 0 intro. intros zenon_H27f zenon_H87 zenon_H27a zenon_H274 zenon_H40 zenon_H268 zenon_H1e7 zenon_H209 zenon_H251 zenon_H234 zenon_H25f zenon_H211 zenon_H62 zenon_H24b zenon_H277 zenon_H279 zenon_H33 zenon_H2e zenon_H28 zenon_H21 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H171 zenon_H16e zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H20b zenon_H145 zenon_H361 zenon_H2fe zenon_H334 zenon_H2fb zenon_H15f zenon_H1ec zenon_H1dd zenon_H1e3 zenon_H312 zenon_H311 zenon_H313 zenon_H1a0 zenon_H18a zenon_H186 zenon_H30e zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H175 zenon_H1ca zenon_H38 zenon_H83 zenon_H17. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H26c. zenon_intro zenon_H280. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_H255. zenon_intro zenon_H281. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.02/33.20 apply (zenon_L125_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.02/33.20 apply (zenon_L9_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.02/33.20 apply (zenon_L234_); trivial. % 33.02/33.20 apply (zenon_L23_); trivial. % 33.02/33.20 (* end of lemma zenon_L236_ *) % 33.02/33.20 assert (zenon_L237_ : ((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.02/33.20 do 0 intro. intros zenon_H2ae zenon_H87 zenon_H31f zenon_H1e7 zenon_H239 zenon_H211 zenon_H4a zenon_H2cd zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_H2c5 zenon_H2c9 zenon_H277 zenon_H279 zenon_H33 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H171 zenon_H16e zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H20b zenon_H145 zenon_H361 zenon_H2fe zenon_H334 zenon_H2fb zenon_H15f zenon_H1ec zenon_H1dd zenon_H1e3 zenon_H312 zenon_H311 zenon_H313 zenon_H1a0 zenon_H18a zenon_H186 zenon_H30e zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H175 zenon_H1ca zenon_H38. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.02/33.20 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.02/33.20 apply (zenon_L7_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.02/33.20 apply (zenon_L196_); trivial. % 33.02/33.20 apply (zenon_L233_); trivial. % 33.02/33.20 apply (zenon_L111_); trivial. % 33.02/33.20 apply (zenon_L124_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.02/33.20 apply (zenon_L9_); trivial. % 33.02/33.20 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.02/33.20 apply (zenon_L234_); trivial. % 33.02/33.20 apply (zenon_L139_); trivial. % 33.02/33.20 (* end of lemma zenon_L237_ *) % 33.02/33.20 assert (zenon_L238_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((h4 (op1 (e11) (e13))) = (op2 (h4 (e11)) (h4 (e13))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H2a4 zenon_H6a zenon_H74 zenon_H6f zenon_H71 zenon_H54 zenon_H4e zenon_H5a zenon_H2b8 zenon_H5e zenon_H73 zenon_H2d0 zenon_H2d1 zenon_H247 zenon_H70 zenon_H83 zenon_H24b zenon_H62 zenon_H25f zenon_H234 zenon_H251 zenon_H268 zenon_H40 zenon_H274 zenon_H27a zenon_H87 zenon_H31f zenon_H1e7 zenon_H239 zenon_H211 zenon_H4a zenon_H2cd zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_H2c5 zenon_H2c9 zenon_H277 zenon_H279 zenon_H33 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H248 zenon_H240 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H171 zenon_H16e zenon_H179 zenon_H2f7 zenon_H2e9 zenon_H168 zenon_H2ef zenon_H198 zenon_H2f4 zenon_H2e3 zenon_H2de zenon_H2e1 zenon_H172 zenon_H19f zenon_H1bf zenon_H126 zenon_H140 zenon_H20b zenon_H145 zenon_H361 zenon_H2fe zenon_H334 zenon_H2fb zenon_H15f zenon_H1ec zenon_H1dd zenon_H1e3 zenon_H312 zenon_H311 zenon_H313 zenon_H1a0 zenon_H18a zenon_H186 zenon_H30e zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H175 zenon_H1ca zenon_H38. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.05/33.21 apply (zenon_L24_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.05/33.21 apply (zenon_L235_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.05/33.21 apply (zenon_L236_); trivial. % 33.05/33.21 apply (zenon_L237_); trivial. % 33.05/33.21 (* end of lemma zenon_L238_ *) % 33.05/33.21 assert (zenon_L239_ : ((h4 (e13)) = (e23)) -> ((op1 (e12) (e10)) = (e13)) -> (~((e23) = (h4 (op1 (e12) (e10))))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H334 zenon_H17f zenon_H36d. % 33.05/33.21 elim (classic ((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [ zenon_intro zenon_H36e | zenon_intro zenon_H36f ]. % 33.05/33.21 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10)))) = ((e23) = (h4 (op1 (e12) (e10))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H36d. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H36e. % 33.05/33.21 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H36f]. % 33.05/33.21 cut (((h4 (op1 (e12) (e10))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H370]. % 33.05/33.21 congruence. % 33.05/33.21 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e12) (e10))) = (e23))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H370. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H334. % 33.05/33.21 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 33.05/33.21 cut (((h4 (e13)) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H371]. % 33.05/33.21 congruence. % 33.05/33.21 elim (classic ((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [ zenon_intro zenon_H36e | zenon_intro zenon_H36f ]. % 33.05/33.21 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10)))) = ((h4 (e13)) = (h4 (op1 (e12) (e10))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H371. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H36e. % 33.05/33.21 cut (((h4 (op1 (e12) (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H36f]. % 33.05/33.21 cut (((h4 (op1 (e12) (e10))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H372]. % 33.05/33.21 congruence. % 33.05/33.21 cut (((op1 (e12) (e10)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H185]. % 33.05/33.21 congruence. % 33.05/33.21 exact (zenon_H185 zenon_H17f). % 33.05/33.21 apply zenon_H36f. apply refl_equal. % 33.05/33.21 apply zenon_H36f. apply refl_equal. % 33.05/33.21 apply zenon_H1da. apply refl_equal. % 33.05/33.21 apply zenon_H36f. apply refl_equal. % 33.05/33.21 apply zenon_H36f. apply refl_equal. % 33.05/33.21 (* end of lemma zenon_L239_ *) % 33.05/33.21 assert (zenon_L240_ : ((op2 (e22) (e20)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((op1 (e12) (e10)) = (e13)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H26d zenon_H2fe zenon_H1dd zenon_H108 zenon_H1a zenon_H334 zenon_H17f zenon_H373. % 33.05/33.21 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H374 | zenon_intro zenon_H375 ]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H373. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H374. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H375]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e10))) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H376]. % 33.05/33.21 congruence. % 33.05/33.21 cut (((op2 (e22) (e20)) = (e23)) = ((op2 (h4 (e12)) (h4 (e10))) = (h4 (op1 (e12) (e10))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H376. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H26d. % 33.05/33.21 cut (((e23) = (h4 (op1 (e12) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H36d]. % 33.05/33.21 cut (((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H377]. % 33.05/33.21 congruence. % 33.05/33.21 elim (classic ((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [ zenon_intro zenon_H374 | zenon_intro zenon_H375 ]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10)))) = ((op2 (e22) (e20)) = (op2 (h4 (e12)) (h4 (e10))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H377. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H374. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (h4 (e12)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H375]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e10))) = (op2 (e22) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H378]. % 33.05/33.21 congruence. % 33.05/33.21 cut (((h4 (e10)) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H107]. % 33.05/33.21 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.05/33.21 congruence. % 33.05/33.21 apply (zenon_L202_); trivial. % 33.05/33.21 apply (zenon_L47_); trivial. % 33.05/33.21 apply zenon_H375. apply refl_equal. % 33.05/33.21 apply zenon_H375. apply refl_equal. % 33.05/33.21 apply (zenon_L239_); trivial. % 33.05/33.21 apply zenon_H375. apply refl_equal. % 33.05/33.21 apply zenon_H375. apply refl_equal. % 33.05/33.21 (* end of lemma zenon_L240_ *) % 33.05/33.21 assert (zenon_L241_ : (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 33.05/33.21 do 0 intro. intros zenon_H18a zenon_H18b zenon_Hf9 zenon_Had zenon_H373 zenon_H334 zenon_H1a zenon_H108 zenon_H1dd zenon_H2fe zenon_H26d zenon_H186 zenon_H12d. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H18a); [ zenon_intro zenon_H18d | zenon_intro zenon_H18c ]. % 33.05/33.21 exact (zenon_H18b zenon_H18d). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H18c); [ zenon_intro zenon_H148 | zenon_intro zenon_H18e ]. % 33.05/33.21 apply (zenon_L59_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H18e); [ zenon_intro zenon_H17f | zenon_intro zenon_H187 ]. % 33.05/33.21 apply (zenon_L240_); trivial. % 33.05/33.21 apply (zenon_L70_); trivial. % 33.05/33.21 (* end of lemma zenon_L241_ *) % 33.05/33.21 assert (zenon_L242_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (e13))) -> (~((e11) = (e13))) -> ((op1 (e11) (e10)) = (e11)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 33.05/33.21 do 0 intro. intros zenon_H274 zenon_H268 zenon_H14 zenon_H32 zenon_H40 zenon_H34 zenon_H17 zenon_H1e7 zenon_H18a zenon_H18b zenon_Hf9 zenon_Had zenon_H373 zenon_H334 zenon_H1a zenon_H108 zenon_H1dd zenon_H2fe zenon_H186 zenon_H12d. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H267 | zenon_intro zenon_H275 ]. % 33.05/33.21 apply (zenon_L120_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H3f | zenon_intro zenon_H276 ]. % 33.05/33.21 apply (zenon_L11_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H26d ]. % 33.05/33.21 apply (zenon_L91_); trivial. % 33.05/33.21 apply (zenon_L241_); trivial. % 33.05/33.21 (* end of lemma zenon_L242_ *) % 33.05/33.21 assert (zenon_L243_ : ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((e11) = (e13))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H19e zenon_H104 zenon_H195 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_H172 zenon_H19 zenon_H1a zenon_H17 zenon_H274 zenon_Hf9 zenon_H373 zenon_H334 zenon_H2fe zenon_H108 zenon_H186 zenon_H18a zenon_H1dd zenon_H1e7 zenon_H34 zenon_H40 zenon_H14 zenon_H268 zenon_H21 zenon_H28 zenon_H2e zenon_Hb1. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.05/33.21 apply (zenon_L30_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.05/33.21 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H1b | zenon_intro zenon_H30 ]. % 33.05/33.21 apply (zenon_L4_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 33.05/33.21 apply (zenon_L242_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H20 | zenon_intro zenon_H27 ]. % 33.05/33.21 apply (zenon_L5_); trivial. % 33.05/33.21 apply (zenon_L6_); trivial. % 33.05/33.21 apply (zenon_L74_); trivial. % 33.05/33.21 (* end of lemma zenon_L243_ *) % 33.05/33.21 assert (zenon_L244_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e22) (e20)) = (e23)) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e12)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 33.05/33.21 do 0 intro. intros zenon_Ha7 zenon_H92 zenon_H373 zenon_H334 zenon_H1a zenon_H108 zenon_H1dd zenon_H2fe zenon_H26d zenon_H1bf zenon_H126 zenon_Had zenon_Hb9 zenon_H1af zenon_H379 zenon_H1b7 zenon_H1a9 zenon_H130 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H12d zenon_H1b6 zenon_H9a zenon_H93 zenon_H90 zenon_Ha1. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H94 | zenon_intro zenon_Ha9 ]. % 33.05/33.21 apply (zenon_L27_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1b6); [ zenon_intro zenon_H131 | zenon_intro zenon_H1b8 ]. % 33.05/33.21 apply (zenon_L55_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1b8); [ zenon_intro zenon_H1a8 | zenon_intro zenon_H1b9 ]. % 33.05/33.21 apply (zenon_L78_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1b9); [ zenon_intro zenon_H1ba | zenon_intro zenon_H118 ]. % 33.05/33.21 exact (zenon_H1b7 zenon_H1ba). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H379); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H37a ]. % 33.05/33.21 apply (zenon_L79_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H37a); [ zenon_intro zenon_Hb8 | zenon_intro zenon_H37b ]. % 33.05/33.21 apply (zenon_L34_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H37b); [ zenon_intro zenon_H1c0 | zenon_intro zenon_H17f ]. % 33.05/33.21 apply (zenon_L84_); trivial. % 33.05/33.21 apply (zenon_L240_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H99 | zenon_intro zenon_Ha0 ]. % 33.05/33.21 apply (zenon_L28_); trivial. % 33.05/33.21 apply (zenon_L29_); trivial. % 33.05/33.21 (* end of lemma zenon_L244_ *) % 33.05/33.21 assert (zenon_L245_ : (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> ((op2 (e21) (e21)) = (e20)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e12)) = (e10))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H274 zenon_H268 zenon_H14 zenon_H32 zenon_H40 zenon_H34 zenon_H17 zenon_H1e7 zenon_Ha7 zenon_H92 zenon_H373 zenon_H334 zenon_H1a zenon_H108 zenon_H1dd zenon_H2fe zenon_H1bf zenon_H126 zenon_Had zenon_Hb9 zenon_H1af zenon_H379 zenon_H1b7 zenon_H1a9 zenon_H130 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H12d zenon_H1b6 zenon_H9a zenon_H93 zenon_H90 zenon_Ha1. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H267 | zenon_intro zenon_H275 ]. % 33.05/33.21 apply (zenon_L120_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H3f | zenon_intro zenon_H276 ]. % 33.05/33.21 apply (zenon_L11_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H26d ]. % 33.05/33.21 apply (zenon_L91_); trivial. % 33.05/33.21 apply (zenon_L244_); trivial. % 33.05/33.21 (* end of lemma zenon_L245_ *) % 33.05/33.21 assert (zenon_L246_ : ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H38 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H172 zenon_H274 zenon_H373 zenon_H334 zenon_H2fe zenon_H108 zenon_H186 zenon_H18a zenon_H1dd zenon_H1e7 zenon_H40 zenon_H14 zenon_H268 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H126 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H140 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H179 zenon_H19f zenon_H1c3 zenon_H1a9 zenon_H379 zenon_H1bf zenon_H1b6 zenon_H1ca zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.05/33.21 apply (zenon_L7_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.05/33.21 apply (zenon_L46_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.21 apply (zenon_L243_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.21 apply (zenon_L32_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.05/33.21 apply (zenon_L66_); trivial. % 33.05/33.21 apply (zenon_L243_); trivial. % 33.05/33.21 apply (zenon_L45_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.05/33.21 apply (zenon_L77_); trivial. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.05/33.21 apply (zenon_L30_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1c0 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.05/33.21 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2e); [ zenon_intro zenon_H1b | zenon_intro zenon_H30 ]. % 33.05/33.21 apply (zenon_L4_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H30); [ zenon_intro zenon_H32 | zenon_intro zenon_H31 ]. % 33.05/33.21 apply (zenon_L245_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H31); [ zenon_intro zenon_H20 | zenon_intro zenon_H27 ]. % 33.05/33.21 apply (zenon_L5_); trivial. % 33.05/33.21 apply (zenon_L6_); trivial. % 33.05/33.21 apply (zenon_L84_); trivial. % 33.05/33.21 (* end of lemma zenon_L246_ *) % 33.05/33.21 assert (zenon_L247_ : ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e21)) = (e22))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (~((e11) = (e13))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e23)) = (e20))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> ((op2 (e23) (e21)) = (e23)) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H19e zenon_H104 zenon_H195 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_H172 zenon_H1e2 zenon_H211 zenon_H20c zenon_H1ec zenon_H68 zenon_H297 zenon_H293 zenon_H40 zenon_H34 zenon_H18a zenon_H186 zenon_H108 zenon_H2fe zenon_H334 zenon_H373 zenon_Hf9 zenon_H274 zenon_H28b zenon_H1fa zenon_H28 zenon_H17 zenon_H1fd zenon_H202 zenon_H201 zenon_H20b zenon_H1e7 zenon_H1a zenon_H1dd zenon_H1e3 zenon_H285 zenon_H2cd zenon_H236 zenon_H2b1 zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_Hb1. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.05/33.21 apply (zenon_L30_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.05/33.21 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H210); [ zenon_intro zenon_H1de | zenon_intro zenon_H212 ]. % 33.05/33.21 exact (zenon_H1e2 zenon_H1de). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H212); [ zenon_intro zenon_H1f0 | zenon_intro zenon_H213 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 33.05/33.21 exact (zenon_H1e2 zenon_H1de). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 33.05/33.21 apply (zenon_L90_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 33.05/33.21 apply (zenon_L91_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H20b); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H20d ]. % 33.05/33.21 apply (zenon_L90_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H20d); [ zenon_intro zenon_H20f | zenon_intro zenon_H20e ]. % 33.05/33.21 exact (zenon_H20c zenon_H20f). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H20e); [ zenon_intro zenon_H1eb | zenon_intro zenon_H1f3 ]. % 33.05/33.21 apply (zenon_L92_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H297); [ zenon_intro zenon_H1fe | zenon_intro zenon_H298 ]. % 33.05/33.21 apply (zenon_L98_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H298); [ zenon_intro zenon_H28a | zenon_intro zenon_H299 ]. % 33.05/33.21 apply (zenon_L131_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H299); [ zenon_intro zenon_H29a | zenon_intro zenon_H1ff ]. % 33.05/33.21 exact (zenon_H1fa zenon_H29a). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H274); [ zenon_intro zenon_H267 | zenon_intro zenon_H275 ]. % 33.05/33.21 apply (zenon_L133_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H275); [ zenon_intro zenon_H3f | zenon_intro zenon_H276 ]. % 33.05/33.21 apply (zenon_L11_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H276); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H26d ]. % 33.05/33.21 apply (zenon_L91_); trivial. % 33.05/33.21 apply (zenon_L241_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H213); [ zenon_intro zenon_H206 | zenon_intro zenon_H20a ]. % 33.05/33.21 apply (zenon_L191_); trivial. % 33.05/33.21 apply (zenon_L193_); trivial. % 33.05/33.21 apply (zenon_L74_); trivial. % 33.05/33.21 (* end of lemma zenon_L247_ *) % 33.05/33.21 assert (zenon_L248_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e20) (e20)) = (e20)))\/((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e23) (e23)) = (e23)))\/((op2 (e23) (e23)) = (e23))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (((op2 (e21) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/((op2 (e21) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> (~((e21) = (e23))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e12) (e10)) = (e13))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> (~((h4 (op1 (e12) (e10))) = (op2 (h4 (e12)) (h4 (e10))))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H2a4 zenon_H6f zenon_H70 zenon_H71 zenon_H5e zenon_H73 zenon_H4a zenon_H4e zenon_H54 zenon_H6a zenon_H74 zenon_H2a5 zenon_H246 zenon_H5a zenon_H22e zenon_H220 zenon_H21c zenon_H22c zenon_H245 zenon_H243 zenon_H83 zenon_H277 zenon_H24b zenon_H62 zenon_H25f zenon_H251 zenon_H27a zenon_H87 zenon_H379 zenon_H268 zenon_H33 zenon_H38 zenon_H247 zenon_H239 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H19e zenon_H195 zenon_H172 zenon_H211 zenon_H1ec zenon_H297 zenon_H40 zenon_H18a zenon_H186 zenon_H108 zenon_H2fe zenon_H334 zenon_H373 zenon_H274 zenon_H28b zenon_H1fd zenon_H201 zenon_H20b zenon_H1e7 zenon_H1dd zenon_H1e3 zenon_H2cd zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H126 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H140 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H179 zenon_H19f zenon_H1c3 zenon_H1bf zenon_H1c4 zenon_H1b6 zenon_H1a9 zenon_H1ca zenon_H234 zenon_H244 zenon_H240 zenon_H248 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H1dc zenon_H279. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.05/33.21 apply (zenon_L24_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H223. zenon_intro zenon_H2ad. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.21 apply (zenon_L246_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.21 apply (zenon_L9_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 33.05/33.21 apply (zenon_L112_); trivial. % 33.05/33.21 apply (zenon_L246_); trivial. % 33.05/33.21 apply (zenon_L23_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.05/33.21 apply (zenon_L127_); trivial. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.21 apply (zenon_L246_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.21 apply (zenon_L9_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.05/33.21 apply (zenon_L7_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H202 | zenon_intro zenon_H235 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H18 | zenon_intro zenon_H236 ]. % 33.05/33.21 apply zenon_H18. apply sym_equal. exact zenon_H17. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.05/33.21 apply (zenon_L46_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.21 apply (zenon_L247_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.21 apply (zenon_L32_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.05/33.21 apply (zenon_L66_); trivial. % 33.05/33.21 apply (zenon_L247_); trivial. % 33.05/33.21 apply (zenon_L45_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.05/33.21 apply (zenon_L77_); trivial. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.05/33.21 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.05/33.21 apply (zenon_L85_); trivial. % 33.05/33.21 apply (zenon_L247_); trivial. % 33.05/33.21 apply (zenon_L109_); trivial. % 33.05/33.21 apply (zenon_L91_); trivial. % 33.05/33.21 apply (zenon_L111_); trivial. % 33.05/33.21 apply (zenon_L137_); trivial. % 33.05/33.21 apply (zenon_L139_); trivial. % 33.05/33.21 (* end of lemma zenon_L248_ *) % 33.05/33.21 assert (zenon_L249_ : (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e21))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e12) (e12)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> ((op1 (e11) (e10)) = (e11)) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e11) (e11)) = (e11))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.05/33.21 do 0 intro. intros zenon_H71 zenon_H75 zenon_H55 zenon_H5e zenon_He8 zenon_Hc7 zenon_Hce zenon_Hc3 zenon_Had zenon_Hb9 zenon_Hcd zenon_Heb zenon_H2fb zenon_H1dd zenon_H2fe zenon_H37c zenon_Hd3 zenon_H90 zenon_H76 zenon_H54 zenon_H40 zenon_H34 zenon_H4a zenon_H5a zenon_H4e zenon_H73 zenon_H62 zenon_H17. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H71); [ zenon_intro zenon_H78 | zenon_intro zenon_H77 ]. % 33.05/33.21 exact (zenon_H75 zenon_H78). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H77); [ zenon_intro zenon_H4b | zenon_intro zenon_H79 ]. % 33.05/33.21 apply (zenon_L15_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H79); [ zenon_intro zenon_H59 | zenon_intro zenon_H63 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H73); [ zenon_intro zenon_H4b | zenon_intro zenon_H7a ]. % 33.05/33.21 apply (zenon_L16_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H7a); [ zenon_intro zenon_H35 | zenon_intro zenon_H7b ]. % 33.05/33.21 exact (zenon_H76 zenon_H35). % 33.05/33.21 apply (zenon_or_s _ _ zenon_H7b); [ zenon_intro zenon_H47 | zenon_intro zenon_H5f ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_He8); [ zenon_intro zenon_Hc4 | zenon_intro zenon_Hf0 ]. % 33.05/33.21 apply (zenon_L38_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hf0); [ zenon_intro zenon_Hae | zenon_intro zenon_Hf1 ]. % 33.05/33.21 exact (zenon_Heb zenon_Hae). % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hf1); [ zenon_intro zenon_Hc0 | zenon_intro zenon_Hd4 ]. % 33.05/33.21 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H37c. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H2fb. % 33.05/33.21 cut (((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H37d]. % 33.05/33.21 cut (((h4 (e11)) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H37e]. % 33.05/33.21 congruence. % 33.05/33.21 elim (classic ((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [ zenon_intro zenon_H37f | zenon_intro zenon_H380 ]. % 33.05/33.21 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11)))) = ((h4 (e11)) = (h4 (op1 (e12) (e11))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H37e. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H37f. % 33.05/33.21 cut (((h4 (op1 (e12) (e11))) = (h4 (op1 (e12) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H380]. % 33.05/33.21 cut (((h4 (op1 (e12) (e11))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H381]. % 33.05/33.21 congruence. % 33.05/33.21 cut (((op1 (e12) (e11)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H382]. % 33.05/33.21 congruence. % 33.05/33.21 exact (zenon_H382 zenon_Hc0). % 33.05/33.21 apply zenon_H380. apply refl_equal. % 33.05/33.21 apply zenon_H380. apply refl_equal. % 33.05/33.21 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H383 | zenon_intro zenon_H384 ]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e23) (e23)) = (op2 (h4 (e12)) (h4 (e11))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H37d. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H383. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H384]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H385]. % 33.05/33.21 congruence. % 33.05/33.21 cut (((op2 (e22) (e21)) = (e21)) = ((op2 (h4 (e12)) (h4 (e11))) = (op2 (e23) (e23)))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H385. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H47. % 33.05/33.21 cut (((e21) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H331]. % 33.05/33.21 cut (((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H386]. % 33.05/33.21 congruence. % 33.05/33.21 elim (classic ((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [ zenon_intro zenon_H383 | zenon_intro zenon_H384 ]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11)))) = ((op2 (e22) (e21)) = (op2 (h4 (e12)) (h4 (e11))))). % 33.05/33.21 intro zenon_D_pnotp. % 33.05/33.21 apply zenon_H386. % 33.05/33.21 rewrite <- zenon_D_pnotp. % 33.05/33.21 exact zenon_H383. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (h4 (e12)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H384]. % 33.05/33.21 cut (((op2 (h4 (e12)) (h4 (e11))) = (op2 (e22) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H387]. % 33.05/33.21 congruence. % 33.05/33.21 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 33.05/33.21 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.05/33.21 congruence. % 33.05/33.21 apply (zenon_L202_); trivial. % 33.05/33.21 apply (zenon_L166_); trivial. % 33.05/33.21 apply zenon_H384. apply refl_equal. % 33.05/33.21 apply zenon_H384. apply refl_equal. % 33.05/33.21 exact (zenon_H331 zenon_H17). % 33.05/33.21 apply zenon_H384. apply refl_equal. % 33.05/33.21 apply zenon_H384. apply refl_equal. % 33.05/33.21 apply (zenon_L40_); trivial. % 33.05/33.21 apply (zenon_L18_); trivial. % 33.05/33.21 apply (zenon_L19_); trivial. % 33.05/33.21 (* end of lemma zenon_L249_ *) % 33.05/33.21 assert (zenon_L250_ : ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (e21))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((op1 (e10) (e10)) = (e10)) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> False). % 33.05/33.21 do 0 intro. intros zenon_He4 zenon_Hb1 zenon_He9 zenon_He6 zenon_Hd7 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H179 zenon_H2de zenon_H2e1 zenon_H1d0 zenon_H172 zenon_H75 zenon_H54 zenon_H4e zenon_H55 zenon_H4a zenon_H17 zenon_H34 zenon_H40 zenon_H73 zenon_H5e zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_H37c zenon_H2fb zenon_H1dd zenon_H2fe zenon_Hd3 zenon_He8 zenon_H76 zenon_H5a zenon_H62 zenon_H71 zenon_Hac zenon_He5 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_H311 zenon_H104 zenon_H313. % 33.05/33.21 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.05/33.21 apply (zenon_L30_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Heb | zenon_intro zenon_Hae ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.05/33.21 apply (zenon_L249_); trivial. % 33.05/33.21 apply (zenon_L159_); trivial. % 33.05/33.21 apply (zenon_L31_); trivial. % 33.05/33.21 apply (zenon_L173_); trivial. % 33.05/33.21 apply (zenon_L27_); trivial. % 33.05/33.21 (* end of lemma zenon_L250_ *) % 33.05/33.21 assert (zenon_L251_ : ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e10)) = (e12))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (e21))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e21) (e20)) = (e21)) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> False). % 33.05/33.21 do 0 intro. intros zenon_He9 zenon_H30e zenon_H2e9 zenon_H168 zenon_H198 zenon_H1d8 zenon_H2f4 zenon_H1d6 zenon_H140 zenon_H126 zenon_H1bf zenon_H2e1 zenon_H2e2 zenon_H172 zenon_H75 zenon_H54 zenon_H4e zenon_H55 zenon_H4a zenon_H17 zenon_H34 zenon_H40 zenon_H73 zenon_H5e zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_H37c zenon_H2fb zenon_H1dd zenon_H2fe zenon_Hd3 zenon_He8 zenon_H76 zenon_H5a zenon_H62 zenon_H71 zenon_Hb1 zenon_Hac zenon_He5 zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7. % 33.05/33.21 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.05/33.21 apply (zenon_L30_); trivial. % 33.05/33.21 apply (zenon_or_s _ _ zenon_He5); [ zenon_intro zenon_Heb | zenon_intro zenon_Hae ]. % 33.05/33.21 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.05/33.21 apply (zenon_L249_); trivial. % 33.05/33.21 apply (zenon_L181_); trivial. % 33.05/33.21 apply (zenon_L32_); trivial. % 33.05/33.21 (* end of lemma zenon_L251_ *) % 33.05/33.21 assert (zenon_L252_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((e11) = (e13))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e21) (e21)) = (e21))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> ((op2 (e21) (e20)) = (e21)) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e22)) = (e21))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e20) (e20)) = (e21))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H1ca zenon_Hdf zenon_H1cb zenon_H311 zenon_H2de zenon_H2e3 zenon_H174 zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_Hf9 zenon_He4 zenon_H1a0 zenon_H195 zenon_H15f zenon_He6 zenon_Hd7 zenon_H179 zenon_H18a zenon_H186 zenon_H19f zenon_H19e zenon_Hfd zenon_H313 zenon_H175 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H16e zenon_H171 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_He5 zenon_Hac zenon_Hb1 zenon_H71 zenon_H62 zenon_H5a zenon_H76 zenon_He8 zenon_Hd3 zenon_H2fe zenon_H1dd zenon_H2fb zenon_H37c zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_H5e zenon_H73 zenon_H40 zenon_H34 zenon_H17 zenon_H4a zenon_H55 zenon_H4e zenon_H54 zenon_H75 zenon_H172 zenon_H2e1 zenon_H1bf zenon_H126 zenon_H140 zenon_H2f4 zenon_H198 zenon_H168 zenon_H2e9 zenon_H30e zenon_He9. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.05/33.22 apply (zenon_L46_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.22 apply (zenon_L250_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.22 apply (zenon_L32_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.05/33.22 apply (zenon_L66_); trivial. % 33.05/33.22 apply (zenon_L250_); trivial. % 33.05/33.22 apply (zenon_L45_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.05/33.22 apply (zenon_L77_); trivial. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.05/33.22 apply (zenon_L251_); trivial. % 33.05/33.22 apply (zenon_L175_); trivial. % 33.05/33.22 (* end of lemma zenon_L252_ *) % 33.05/33.22 assert (zenon_L253_ : ((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23))))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H2a8 zenon_H6f zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H70 zenon_H33 zenon_H74 zenon_H2d1 zenon_H2d0 zenon_H2b8 zenon_H6a zenon_H31f zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H179 zenon_H2de zenon_H2e1 zenon_H172 zenon_H54 zenon_H4e zenon_H4a zenon_H40 zenon_H73 zenon_H5e zenon_H37c zenon_H2fb zenon_H1dd zenon_H2fe zenon_H5a zenon_H62 zenon_H71 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H195 zenon_H18a zenon_H186 zenon_H19f zenon_H19e zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H1e7 zenon_H247 zenon_H38. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.05/33.22 apply (zenon_L7_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H55 | zenon_intro zenon_H69 ]. % 33.05/33.22 apply (zenon_L252_); trivial. % 33.05/33.22 apply (zenon_L206_); trivial. % 33.05/33.22 apply (zenon_L91_); trivial. % 33.05/33.22 apply (zenon_L8_); trivial. % 33.05/33.22 apply (zenon_L4_); trivial. % 33.05/33.22 (* end of lemma zenon_L253_ *) % 33.05/33.22 assert (zenon_L254_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((op2 (e20) (e20)) = (e20)) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H6f zenon_H74 zenon_H210 zenon_H2be zenon_H23a zenon_H209 zenon_H2b1 zenon_H2cd zenon_H285 zenon_H1e3 zenon_H1e7 zenon_H211 zenon_H239 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H179 zenon_H2de zenon_H2e1 zenon_H172 zenon_H54 zenon_H4e zenon_H4a zenon_H40 zenon_H73 zenon_H5e zenon_H37c zenon_H2fb zenon_H1dd zenon_H2fe zenon_H5a zenon_H62 zenon_H71 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H195 zenon_H18a zenon_H186 zenon_H19f zenon_H19e zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H38 zenon_H33 zenon_H70 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H277 zenon_H14 zenon_H279. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.05/33.22 apply (zenon_L7_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H55 | zenon_intro zenon_H69 ]. % 33.05/33.22 apply (zenon_L252_); trivial. % 33.05/33.22 apply (zenon_L194_); trivial. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_L124_); trivial. % 33.05/33.22 apply (zenon_L4_); trivial. % 33.05/33.22 (* end of lemma zenon_L254_ *) % 33.05/33.22 assert (zenon_L255_ : ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((e10) = (e13))) -> (~((e12) = (e13))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((e11) = (e13))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((op2 (e22) (e22)) = (e22)) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H6f zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H70 zenon_H33 zenon_H38 zenon_H1ca zenon_H2f4 zenon_H2e9 zenon_H30e zenon_H19e zenon_H19f zenon_H186 zenon_H18a zenon_H195 zenon_H198 zenon_H1a0 zenon_H171 zenon_H16e zenon_H173 zenon_H145 zenon_H160 zenon_H14e zenon_H153 zenon_H161 zenon_H15f zenon_H130 zenon_H12c zenon_H128 zenon_H11d zenon_H132 zenon_H139 zenon_H174 zenon_H168 zenon_H175 zenon_H1cb zenon_H313 zenon_H311 zenon_H71 zenon_H62 zenon_H5a zenon_H2fe zenon_H1dd zenon_H2fb zenon_H37c zenon_H5e zenon_H73 zenon_H40 zenon_H4a zenon_H4e zenon_H54 zenon_H172 zenon_H2e1 zenon_H2de zenon_H179 zenon_H2e3 zenon_H1bf zenon_H126 zenon_H140 zenon_Hfd zenon_Hf9 zenon_He9 zenon_Hdf zenon_Hcd zenon_Hc7 zenon_Hc3 zenon_Hb9 zenon_He8 zenon_Hd3 zenon_Hd7 zenon_He6 zenon_He5 zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H6a zenon_H68 zenon_H74. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.05/33.22 apply (zenon_L7_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H74); [ zenon_intro zenon_H55 | zenon_intro zenon_H69 ]. % 33.05/33.22 apply (zenon_L252_); trivial. % 33.05/33.22 apply (zenon_L20_); trivial. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_L4_); trivial. % 33.05/33.22 (* end of lemma zenon_L255_ *) % 33.05/33.22 assert (zenon_L256_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> (~((e21) = (e23))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e11))) = (op2 (h4 (e12)) (h4 (e11))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H2a4 zenon_H247 zenon_H31f zenon_H2b8 zenon_H2d0 zenon_H2d1 zenon_H83 zenon_H248 zenon_H240 zenon_H24b zenon_H25f zenon_H234 zenon_H251 zenon_H20b zenon_H268 zenon_H274 zenon_H27a zenon_H87 zenon_H279 zenon_H277 zenon_H239 zenon_H211 zenon_H1e7 zenon_H1e3 zenon_H2cd zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_H74 zenon_H6a zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H140 zenon_H126 zenon_H1bf zenon_H2e3 zenon_H179 zenon_H2de zenon_H2e1 zenon_H172 zenon_H54 zenon_H4e zenon_H4a zenon_H40 zenon_H73 zenon_H5e zenon_H37c zenon_H2fb zenon_H1dd zenon_H2fe zenon_H5a zenon_H62 zenon_H71 zenon_H311 zenon_H313 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H195 zenon_H18a zenon_H186 zenon_H19f zenon_H19e zenon_H30e zenon_H2e9 zenon_H2f4 zenon_H1ca zenon_H38 zenon_H33 zenon_H70 zenon_H19 zenon_H1a zenon_H17 zenon_H21 zenon_H28 zenon_H2e zenon_H6f. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.05/33.22 apply (zenon_L24_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.05/33.22 apply (zenon_L253_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.05/33.22 apply (zenon_L127_); trivial. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_L254_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_L255_); trivial. % 33.05/33.22 apply (zenon_L139_); trivial. % 33.05/33.22 (* end of lemma zenon_L256_ *) % 33.05/33.22 assert (zenon_L257_ : ((op2 (e22) (e22)) = (e22)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e12)) (h4 (e12))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H68 zenon_H2fe zenon_H1dd zenon_H388. % 33.05/33.22 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H389 | zenon_intro zenon_H38a ]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e12)) (h4 (e12))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H388. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H389. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H38a]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H38b]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((op2 (e22) (e22)) = (e22)) = ((op2 (h4 (e12)) (h4 (e12))) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H38b. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H68. % 33.05/33.22 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))))); [idtac | apply NNPP; zenon_intro zenon_H308]. % 33.05/33.22 cut (((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H38c]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [ zenon_intro zenon_H389 | zenon_intro zenon_H38a ]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12)))) = ((op2 (e22) (e22)) = (op2 (h4 (e12)) (h4 (e12))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H38c. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H389. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H38a]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e12))) = (op2 (e22) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H38d]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.05/33.22 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.05/33.22 congruence. % 33.05/33.22 apply (zenon_L202_); trivial. % 33.05/33.22 apply (zenon_L202_); trivial. % 33.05/33.22 apply zenon_H38a. apply refl_equal. % 33.05/33.22 apply zenon_H38a. apply refl_equal. % 33.05/33.22 exact (zenon_H308 zenon_H1dd). % 33.05/33.22 apply zenon_H38a. apply refl_equal. % 33.05/33.22 apply zenon_H38a. apply refl_equal. % 33.05/33.22 (* end of lemma zenon_L257_ *) % 33.05/33.22 assert (zenon_L258_ : (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((op1 (e12) (e12)) = (e12)) -> ((op2 (e22) (e22)) = (e22)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H38e zenon_Hdd zenon_H68 zenon_H2fe zenon_H1dd. % 33.05/33.22 cut (((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H38e. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H2fe. % 33.05/33.22 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e12)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H388]. % 33.05/33.22 cut (((h4 (e12)) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H38f]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [ zenon_intro zenon_H390 | zenon_intro zenon_H391 ]. % 33.05/33.22 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12)))) = ((h4 (e12)) = (h4 (op1 (e12) (e12))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H38f. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H390. % 33.05/33.22 cut (((h4 (op1 (e12) (e12))) = (h4 (op1 (e12) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H391]. % 33.05/33.22 cut (((h4 (op1 (e12) (e12))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H392]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((op1 (e12) (e12)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H19c]. % 33.05/33.22 congruence. % 33.05/33.22 exact (zenon_H19c zenon_Hdd). % 33.05/33.22 apply zenon_H391. apply refl_equal. % 33.05/33.22 apply zenon_H391. apply refl_equal. % 33.05/33.22 apply (zenon_L257_); trivial. % 33.05/33.22 (* end of lemma zenon_L258_ *) % 33.05/33.22 assert (zenon_L259_ : (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((e11) = (e13))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e22) (e22)) = (e22)) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H1ca zenon_He5 zenon_Hd3 zenon_He8 zenon_Hdf zenon_H2de zenon_H2e3 zenon_H1a0 zenon_H15f zenon_H18a zenon_H186 zenon_H16e zenon_H171 zenon_Hfd zenon_H313 zenon_H311 zenon_H312 zenon_H1bf zenon_H126 zenon_H172 zenon_H2e1 zenon_Hc3 zenon_H140 zenon_H2f4 zenon_H198 zenon_H168 zenon_H2e9 zenon_H30e zenon_Hcd zenon_Hc7 zenon_Hb9 zenon_H179 zenon_Hf9 zenon_H2ef zenon_H19f zenon_Hd7 zenon_He6 zenon_H2f7 zenon_He9 zenon_H195 zenon_H19e zenon_He4 zenon_Ha7 zenon_Ha1 zenon_H9a zenon_H90 zenon_H93 zenon_H92 zenon_Hac zenon_Hb1 zenon_H1dd zenon_H2fe zenon_H68 zenon_H38e. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.05/33.22 apply (zenon_L46_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.05/33.22 apply (zenon_L30_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 33.05/33.22 apply (zenon_L165_); trivial. % 33.05/33.22 apply (zenon_L258_); trivial. % 33.05/33.22 apply (zenon_L74_); trivial. % 33.05/33.22 apply (zenon_L173_); trivial. % 33.05/33.22 apply (zenon_L27_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.22 apply (zenon_L32_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.22 apply (zenon_L258_); trivial. % 33.05/33.22 apply (zenon_L45_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.05/33.22 apply (zenon_L77_); trivial. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_He4); [ zenon_intro zenon_Hea | zenon_intro zenon_H94 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H313); [ zenon_intro zenon_H2e2 | zenon_intro zenon_H131 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H19e); [ zenon_intro zenon_H18b | zenon_intro zenon_H14c ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hb1); [ zenon_intro zenon_Ha8 | zenon_intro zenon_Had ]. % 33.05/33.22 apply (zenon_L30_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_He9); [ zenon_intro zenon_Hce | zenon_intro zenon_Hde ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H312); [ zenon_intro zenon_H19c | zenon_intro zenon_Hdd ]. % 33.05/33.22 apply (zenon_L184_); trivial. % 33.05/33.22 apply (zenon_L258_); trivial. % 33.05/33.22 apply (zenon_L181_); trivial. % 33.05/33.22 apply (zenon_L74_); trivial. % 33.05/33.22 apply (zenon_L173_); trivial. % 33.05/33.22 apply (zenon_L27_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.22 apply (zenon_L32_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.22 apply (zenon_L258_); trivial. % 33.05/33.22 apply (zenon_L186_); trivial. % 33.05/33.22 (* end of lemma zenon_L259_ *) % 33.05/33.22 assert (zenon_L260_ : ((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23))))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> (~((e21) = (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H86 zenon_H87 zenon_H2e zenon_H28 zenon_H21 zenon_H1a zenon_H19 zenon_H33 zenon_H38 zenon_H38e zenon_H2fe zenon_H1dd zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_H19e zenon_H195 zenon_He9 zenon_H2f7 zenon_He6 zenon_Hd7 zenon_H19f zenon_H2ef zenon_Hf9 zenon_H179 zenon_Hb9 zenon_Hc7 zenon_Hcd zenon_H30e zenon_H2e9 zenon_H168 zenon_H198 zenon_H2f4 zenon_H140 zenon_Hc3 zenon_H2e1 zenon_H172 zenon_H126 zenon_H1bf zenon_H312 zenon_H311 zenon_H313 zenon_Hfd zenon_H171 zenon_H16e zenon_H186 zenon_H18a zenon_H15f zenon_H1a0 zenon_H2e3 zenon_H2de zenon_Hdf zenon_He8 zenon_Hd3 zenon_He5 zenon_H1ca zenon_H83 zenon_H17. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H13. zenon_intro zenon_H88. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_L2_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_L259_); trivial. % 33.05/33.22 apply (zenon_L23_); trivial. % 33.05/33.22 (* end of lemma zenon_L260_ *) % 33.05/33.22 assert (zenon_L261_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e22) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e23)))) -> ((~((op2 (e22) (e22)) = (e23)))\/((op2 (e22) (e23)) = (e22))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (~((e21) = (e23))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/((op2 (e23) (e21)) = (e22))))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e20) (e23)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e22) (e20)) = (e23))))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e20) (e23)) = (e21))\/(((op2 (e20) (e23)) = (e22))\/((op2 (e20) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e22) (e22)) = (e22)))\/((op2 (e22) (e22)) = (e22))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e21) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e21))\/(((op2 (e21) (e23)) = (e22))\/((op2 (e21) (e23)) = (e23))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e21) (e23)) = (op2 (e22) (e23)))) -> (((op2 (e22) (e20)) = (e22))\/(((op2 (e22) (e21)) = (e22))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e22) (e23)) = (e22))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e22)))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> ((e21) = (op2 (e23) (e23))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((h4 (op1 (e12) (e12))) = (op2 (h4 (e12)) (h4 (e12))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (((op1 (e12) (e10)) = (e12))\/(((op1 (e12) (e11)) = (e12))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e12) (e13)) = (e12))))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e11) (e13)) = (op1 (e12) (e13)))) -> (~((e11) = (e13))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e10) (e11)) = (e12))\/(((op1 (e10) (e12)) = (e12))\/((op1 (e10) (e13)) = (e12))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (((op1 (e11) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e11))\/(((op1 (e11) (e13)) = (e12))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (((op1 (e10) (e10)) = (e12))\/(((op1 (e11) (e10)) = (e12))\/(((op1 (e12) (e10)) = (e12))\/((op1 (e13) (e10)) = (e12))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e12)))\/((op1 (e12) (e12)) = (e12))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e12)))) -> ((~((op1 (e10) (e10)) = (e12)))\/((op1 (e10) (e12)) = (e10))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e11)) = (e12))\/((op1 (e10) (e11)) = (e13))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H2a4 zenon_H6f zenon_H71 zenon_H54 zenon_H4e zenon_H5a zenon_H2b8 zenon_H5e zenon_H73 zenon_H2d0 zenon_H2d1 zenon_H247 zenon_H70 zenon_H83 zenon_H248 zenon_H240 zenon_H24b zenon_H62 zenon_H25f zenon_H234 zenon_H251 zenon_H20b zenon_H268 zenon_H40 zenon_H274 zenon_H27a zenon_H87 zenon_H31f zenon_H1e7 zenon_H239 zenon_H211 zenon_H4a zenon_H1e3 zenon_H2cd zenon_H209 zenon_H23a zenon_H2be zenon_H210 zenon_H2c5 zenon_H2c9 zenon_H277 zenon_H279 zenon_H2e zenon_H28 zenon_H21 zenon_H17 zenon_H1a zenon_H19 zenon_H33 zenon_H38 zenon_H38e zenon_H2fe zenon_H1dd zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_H19e zenon_H195 zenon_He9 zenon_H2f7 zenon_He6 zenon_Hd7 zenon_H19f zenon_H2ef zenon_Hf9 zenon_H179 zenon_Hb9 zenon_Hc7 zenon_Hcd zenon_H30e zenon_H2e9 zenon_H168 zenon_H198 zenon_H2f4 zenon_H140 zenon_Hc3 zenon_H2e1 zenon_H172 zenon_H126 zenon_H1bf zenon_H312 zenon_H311 zenon_H313 zenon_Hfd zenon_H171 zenon_H16e zenon_H186 zenon_H18a zenon_H15f zenon_H1a0 zenon_H2e3 zenon_H2de zenon_Hdf zenon_He8 zenon_Hd3 zenon_He5 zenon_H1ca. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.05/33.22 apply (zenon_L260_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H6f); [ zenon_intro zenon_H75 | zenon_intro zenon_H1b ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H38); [ zenon_intro zenon_H2f | zenon_intro zenon_H34 ]. % 33.05/33.22 apply (zenon_L7_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H70); [ zenon_intro zenon_H76 | zenon_intro zenon_H35 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H248); [ zenon_intro zenon_H20c | zenon_intro zenon_H241 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.05/33.22 apply (zenon_L153_); trivial. % 33.05/33.22 apply (zenon_L259_); trivial. % 33.05/33.22 apply (zenon_L91_); trivial. % 33.05/33.22 apply (zenon_L111_); trivial. % 33.05/33.22 apply (zenon_L8_); trivial. % 33.05/33.22 apply (zenon_L124_); trivial. % 33.05/33.22 apply (zenon_L4_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_L259_); trivial. % 33.05/33.22 apply (zenon_L23_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H26c. zenon_intro zenon_H280. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_H255. zenon_intro zenon_H281. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_L125_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_L259_); trivial. % 33.05/33.22 apply (zenon_L23_); trivial. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H31f); [ zenon_intro zenon_H27e | zenon_intro zenon_H68 ]. % 33.05/33.22 apply (zenon_L196_); trivial. % 33.05/33.22 apply (zenon_L259_); trivial. % 33.05/33.22 apply (zenon_L124_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_L259_); trivial. % 33.05/33.22 apply (zenon_L139_); trivial. % 33.05/33.22 (* end of lemma zenon_L261_ *) % 33.05/33.22 assert (zenon_L262_ : ((op2 (e22) (e23)) = (e20)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H29c zenon_H2fe zenon_H1dd zenon_H334 zenon_H1a zenon_H393. % 33.05/33.22 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H394 | zenon_intro zenon_H395 ]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H393. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H394. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H395]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H396]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((op2 (e22) (e23)) = (e20)) = ((op2 (h4 (e12)) (h4 (e13))) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H396. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H29c. % 33.05/33.22 cut (((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))); [idtac | apply NNPP; zenon_intro zenon_H114]. % 33.05/33.22 cut (((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H397]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [ zenon_intro zenon_H394 | zenon_intro zenon_H395 ]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13)))) = ((op2 (e22) (e23)) = (op2 (h4 (e12)) (h4 (e13))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H397. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H394. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H395]. % 33.05/33.22 cut (((op2 (h4 (e12)) (h4 (e13))) = (op2 (e22) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H398]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 33.05/33.22 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.05/33.22 congruence. % 33.05/33.22 apply (zenon_L202_); trivial. % 33.05/33.22 exact (zenon_H340 zenon_H334). % 33.05/33.22 apply zenon_H395. apply refl_equal. % 33.05/33.22 apply zenon_H395. apply refl_equal. % 33.05/33.22 exact (zenon_H114 zenon_H1a). % 33.05/33.22 apply zenon_H395. apply refl_equal. % 33.05/33.22 apply zenon_H395. apply refl_equal. % 33.05/33.22 (* end of lemma zenon_L262_ *) % 33.05/33.22 assert (zenon_L263_ : (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op1 (e12) (e13)) = (e10)) -> ((op2 (e22) (e23)) = (e20)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> False). % 33.05/33.22 do 0 intro. intros zenon_H399 zenon_H108 zenon_H39a zenon_H29c zenon_H1a zenon_H2fe zenon_H1dd zenon_H334. % 33.05/33.22 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H399. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H108. % 33.05/33.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (op2 (h4 (e12)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H393]. % 33.05/33.22 cut (((h4 (e10)) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H39b]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [ zenon_intro zenon_H39c | zenon_intro zenon_H39d ]. % 33.05/33.22 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13)))) = ((h4 (e10)) = (h4 (op1 (e12) (e13))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H39b. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H39c. % 33.05/33.22 cut (((h4 (op1 (e12) (e13))) = (h4 (op1 (e12) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H39d]. % 33.05/33.22 cut (((h4 (op1 (e12) (e13))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H39e]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((op1 (e12) (e13)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H39f]. % 33.05/33.22 congruence. % 33.05/33.22 exact (zenon_H39f zenon_H39a). % 33.05/33.22 apply zenon_H39d. apply refl_equal. % 33.05/33.22 apply zenon_H39d. apply refl_equal. % 33.05/33.22 apply (zenon_L262_); trivial. % 33.05/33.22 (* end of lemma zenon_L263_ *) % 33.05/33.22 assert (zenon_L264_ : (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((op1 (e13) (e13)) = (e10))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H3a0 zenon_H104 zenon_H195 zenon_H2e9 zenon_H90 zenon_H93 zenon_H334 zenon_H1dd zenon_H2fe zenon_H1a zenon_H29c zenon_H108 zenon_H399 zenon_H3a1. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a0); [ zenon_intro zenon_H14c | zenon_intro zenon_H3a2 ]. % 33.05/33.22 apply (zenon_L74_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a2); [ zenon_intro zenon_H2e8 | zenon_intro zenon_H3a3 ]. % 33.05/33.22 apply (zenon_L160_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a3); [ zenon_intro zenon_H39a | zenon_intro zenon_H3a4 ]. % 33.05/33.22 apply (zenon_L263_); trivial. % 33.05/33.22 exact (zenon_H3a1 zenon_H3a4). % 33.05/33.22 (* end of lemma zenon_L264_ *) % 33.05/33.22 assert (zenon_L265_ : ((~((op1 (e13) (e13)) = (e10)))\/((op1 (e13) (e10)) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op2 (e23) (e23)) = (e20))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H3a5 zenon_H186 zenon_H172 zenon_H24b zenon_H14 zenon_H2be zenon_H1a zenon_H17 zenon_H3a0 zenon_H2fe zenon_H1dd zenon_H334 zenon_H108 zenon_H399 zenon_H90 zenon_H93 zenon_H2e9 zenon_H104 zenon_H195 zenon_H202 zenon_H3a6. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a5); [ zenon_intro zenon_H3a1 | zenon_intro zenon_H187 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a6); [ zenon_intro zenon_H21a | zenon_intro zenon_H3a7 ]. % 33.05/33.22 apply (zenon_L113_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a7); [ zenon_intro zenon_H2bd | zenon_intro zenon_H3a8 ]. % 33.05/33.22 apply (zenon_L145_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a8); [ zenon_intro zenon_H29c | zenon_intro zenon_H205 ]. % 33.05/33.22 apply (zenon_L264_); trivial. % 33.05/33.22 exact (zenon_H202 zenon_H205). % 33.05/33.22 apply (zenon_L71_); trivial. % 33.05/33.22 (* end of lemma zenon_L265_ *) % 33.05/33.22 assert (zenon_L266_ : (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((h4 (e13)) = (e23)) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op2 (e22) (e23)) = (e20)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> (~((op1 (e12) (e12)) = (e10))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> ((op1 (e13) (e11)) = (e13)) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> False). % 33.05/33.22 do 0 intro. intros zenon_Ha7 zenon_H92 zenon_H334 zenon_H1dd zenon_H2fe zenon_H1a zenon_H29c zenon_H108 zenon_H399 zenon_H1b7 zenon_H1b6 zenon_H12d zenon_H12c zenon_H126 zenon_H128 zenon_H11d zenon_H132 zenon_H130 zenon_H1a9 zenon_H1af zenon_H3a9 zenon_H9a zenon_H93 zenon_H90 zenon_Ha1. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Ha7); [ zenon_intro zenon_H94 | zenon_intro zenon_Ha9 ]. % 33.05/33.22 apply (zenon_L27_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Ha9); [ zenon_intro zenon_Hab | zenon_intro zenon_Haa ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a9); [ zenon_intro zenon_H1b0 | zenon_intro zenon_H3aa ]. % 33.05/33.22 apply (zenon_L80_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3aa); [ zenon_intro zenon_H99 | zenon_intro zenon_H3ab ]. % 33.05/33.22 apply (zenon_L28_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3ab); [ zenon_intro zenon_H1ba | zenon_intro zenon_H39a ]. % 33.05/33.22 exact (zenon_H1b7 zenon_H1ba). % 33.05/33.22 apply (zenon_L263_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Haa); [ zenon_intro zenon_H99 | zenon_intro zenon_Ha0 ]. % 33.05/33.22 apply (zenon_L28_); trivial. % 33.05/33.22 apply (zenon_L29_); trivial. % 33.05/33.22 (* end of lemma zenon_L266_ *) % 33.05/33.22 assert (zenon_L267_ : ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((~((op1 (e13) (e13)) = (e10)))\/((op1 (e13) (e10)) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> ((op2 (e20) (e20)) = (e20)) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((e11) = (op1 (e13) (e13))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H244 zenon_H234 zenon_H239 zenon_H3a5 zenon_H186 zenon_H172 zenon_H24b zenon_H14 zenon_H2be zenon_H1a zenon_H17 zenon_H3a0 zenon_H2fe zenon_H1dd zenon_H334 zenon_H108 zenon_H399 zenon_H90 zenon_H93 zenon_H2e9 zenon_H195 zenon_H3a6 zenon_Hb1 zenon_Hac zenon_H92 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H126 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H140 zenon_H173 zenon_H16e zenon_H171 zenon_H1b6 zenon_H1a9 zenon_H3a9 zenon_H1bf zenon_H1c3 zenon_H1ca. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H202 | zenon_intro zenon_H235 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_Hfc). zenon_intro zenon_Hff. zenon_intro zenon_Hfe. % 33.05/33.22 apply (zenon_and_s _ _ zenon_Hfe). zenon_intro zenon_H101. zenon_intro zenon_H100. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H100). zenon_intro zenon_He7. zenon_intro zenon_H102. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.22 apply (zenon_L265_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.22 apply (zenon_L32_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.22 apply (zenon_L43_); trivial. % 33.05/33.22 apply (zenon_L45_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.22 apply (zenon_L265_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.22 apply (zenon_L32_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.05/33.22 apply (zenon_L66_); trivial. % 33.05/33.22 apply (zenon_L265_); trivial. % 33.05/33.22 apply (zenon_L45_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H19d). zenon_intro zenon_H17e. zenon_intro zenon_H1a1. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1a1). zenon_intro zenon_H18f. zenon_intro zenon_H1a2. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1a2). zenon_intro zenon_H19b. zenon_intro zenon_H1a3. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.22 apply (zenon_L265_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.22 apply (zenon_L32_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.22 apply (zenon_L76_); trivial. % 33.05/33.22 apply (zenon_L45_); trivial. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1c3); [ zenon_intro zenon_H1b7 | zenon_intro zenon_H1c0 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.05/33.22 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a6); [ zenon_intro zenon_H21a | zenon_intro zenon_H3a7 ]. % 33.05/33.22 apply (zenon_L113_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a7); [ zenon_intro zenon_H2bd | zenon_intro zenon_H3a8 ]. % 33.05/33.22 apply (zenon_L145_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a8); [ zenon_intro zenon_H29c | zenon_intro zenon_H205 ]. % 33.05/33.22 apply (zenon_L266_); trivial. % 33.05/33.22 exact (zenon_H202 zenon_H205). % 33.05/33.22 apply (zenon_L84_); trivial. % 33.05/33.22 apply (zenon_L109_); trivial. % 33.05/33.22 (* end of lemma zenon_L267_ *) % 33.05/33.22 assert (zenon_L268_ : ((~((op1 (e13) (e13)) = (e10)))\/((op1 (e13) (e10)) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e20) (e20)) = (e22))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> ((op1 (e10) (e10)) = (e10)) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e23) (e23)) = (e20))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (~((op2 (e22) (e22)) = (e20))) -> (~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H3a5 zenon_H186 zenon_H172 zenon_H1e2 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H1e7 zenon_H29f zenon_H195 zenon_H104 zenon_H2e9 zenon_H93 zenon_H90 zenon_H399 zenon_H108 zenon_H334 zenon_H2fe zenon_H3a0 zenon_H21 zenon_H201 zenon_H202 zenon_H1fd zenon_H17 zenon_H28 zenon_H285 zenon_H28b zenon_H1fa zenon_H293 zenon_H297 zenon_H211. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3a5); [ zenon_intro zenon_H3a1 | zenon_intro zenon_H187 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H211); [ zenon_intro zenon_H1de | zenon_intro zenon_H214 ]. % 33.05/33.22 exact (zenon_H1e2 zenon_H1de). % 33.05/33.22 apply (zenon_or_s _ _ zenon_H214); [ zenon_intro zenon_H1e4 | zenon_intro zenon_H215 ]. % 33.05/33.22 apply (zenon_L90_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H215); [ zenon_intro zenon_H1e8 | zenon_intro zenon_H1f7 ]. % 33.05/33.22 apply (zenon_L91_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H29f); [ zenon_intro zenon_H267 | zenon_intro zenon_H2a0 ]. % 33.05/33.22 apply (zenon_L134_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a0); [ zenon_intro zenon_H20 | zenon_intro zenon_H2a1 ]. % 33.05/33.22 apply (zenon_L5_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a1); [ zenon_intro zenon_H29a | zenon_intro zenon_H29c ]. % 33.05/33.22 exact (zenon_H1fa zenon_H29a). % 33.05/33.22 apply (zenon_L264_); trivial. % 33.05/33.22 apply (zenon_L71_); trivial. % 33.05/33.22 (* end of lemma zenon_L268_ *) % 33.05/33.22 assert (zenon_L269_ : (((~((op2 (e20) (op2 (e20) (e20))) = (op2 (e20) (e20))))/\((~((op2 (e21) (op2 (e20) (e21))) = (op2 (e20) (e21))))/\((~((op2 (e22) (op2 (e20) (e22))) = (op2 (e20) (e22))))/\(~((op2 (e23) (op2 (e20) (e23))) = (op2 (e20) (e23)))))))\/(((~((op2 (e20) (op2 (e21) (e20))) = (op2 (e21) (e20))))/\((~((op2 (e21) (op2 (e21) (e21))) = (op2 (e21) (e21))))/\((~((op2 (e22) (op2 (e21) (e22))) = (op2 (e21) (e22))))/\(~((op2 (e23) (op2 (e21) (e23))) = (op2 (e21) (e23)))))))\/(((~((op2 (e20) (op2 (e22) (e20))) = (op2 (e22) (e20))))/\((~((op2 (e21) (op2 (e22) (e21))) = (op2 (e22) (e21))))/\((~((op2 (e22) (op2 (e22) (e22))) = (op2 (e22) (e22))))/\(~((op2 (e23) (op2 (e22) (e23))) = (op2 (e22) (e23)))))))\/((~((op2 (e20) (op2 (e23) (e20))) = (op2 (e23) (e20))))/\((~((op2 (e21) (op2 (e23) (e21))) = (op2 (e23) (e21))))/\((~((op2 (e22) (op2 (e23) (e22))) = (op2 (e23) (e22))))/\(~((op2 (e23) (op2 (e23) (e23))) = (op2 (e23) (e23)))))))))) -> ((~((op2 (e20) (e20)) = (e21)))\/((op2 (e20) (e21)) = (e20))) -> ((~((op2 (e21) (e21)) = (e21)))\/((op2 (e21) (e21)) = (e21))) -> (((op2 (e20) (e20)) = (e21))\/(((op2 (e20) (e21)) = (e21))\/(((op2 (e20) (e22)) = (e21))\/((op2 (e20) (e23)) = (e21))))) -> (~((op2 (e20) (e23)) = (op2 (e23) (e23)))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e23)))) -> (((op2 (e20) (e21)) = (e21))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/((op2 (e23) (e21)) = (e21))))) -> (~((op2 (e21) (e20)) = (op2 (e22) (e20)))) -> (~((op2 (e20) (e21)) = (op2 (e22) (e21)))) -> (~((op2 (e22) (e23)) = (op2 (e23) (e23)))) -> (((op2 (e22) (e20)) = (e21))\/(((op2 (e22) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e21))\/((op2 (e22) (e23)) = (e21))))) -> (~((op2 (e22) (e21)) = (op2 (e22) (e22)))) -> ((~((op2 (e22) (e22)) = (e21)))\/((op2 (e22) (e21)) = (e22))) -> ((~((op2 (e20) (e20)) = (e20)))\/((op2 (e20) (e20)) = (e20))) -> ((~((op2 (e21) (e21)) = (e22)))\/((op2 (e21) (e22)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e22)))) -> ((~((op2 (e23) (e23)) = (e23)))\/((op2 (e23) (e23)) = (e23))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e20) (e21)) = (e22))\/(((op2 (e20) (e22)) = (e22))\/((op2 (e20) (e23)) = (e22))))) -> (~((op2 (e20) (e23)) = (op2 (e21) (e23)))) -> (~((op2 (e20) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e21) (e20)) = (e22))\/(((op2 (e21) (e21)) = (e22))\/(((op2 (e21) (e22)) = (e22))\/((op2 (e21) (e23)) = (e22))))) -> (~((op2 (e21) (e22)) = (op2 (e22) (e22)))) -> (((op2 (e20) (e23)) = (e23))\/(((op2 (e21) (e23)) = (e23))\/(((op2 (e22) (e23)) = (e23))\/((op2 (e23) (e23)) = (e23))))) -> (~((e22) = (e23))) -> (~((e20) = (e23))) -> (((op2 (e21) (e20)) = (e23))\/(((op2 (e21) (e21)) = (e23))\/(((op2 (e21) (e22)) = (e23))\/((op2 (e21) (e23)) = (e23))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e20) (e21)) = (e20))\/(((op2 (e20) (e22)) = (e20))\/((op2 (e20) (e23)) = (e20))))) -> (~((op2 (e21) (e23)) = (op2 (e23) (e23)))) -> ((~((op2 (e21) (e21)) = (e23)))\/((op2 (e21) (e23)) = (e21))) -> (~((e21) = (e23))) -> ((~((op2 (e21) (e21)) = (e20)))\/((op2 (e21) (e20)) = (e21))) -> (~((op2 (e21) (e20)) = (op2 (e21) (e21)))) -> (~((op2 (e20) (e21)) = (op2 (e21) (e21)))) -> (((op2 (e20) (e21)) = (e20))\/(((op2 (e21) (e21)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/((op2 (e23) (e21)) = (e20))))) -> (~((op2 (e20) (e20)) = (op2 (e20) (e23)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e23)))) -> (((op2 (e20) (e23)) = (e20))\/(((op2 (e21) (e23)) = (e20))\/(((op2 (e22) (e23)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (((op1 (e12) (e10)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e12) (e13)) = (e10))))) -> (((op2 (e20) (e20)) = (e20))\/(((op2 (e21) (e21)) = (e21))\/(((op2 (e22) (e22)) = (e22))\/((op2 (e23) (e23)) = (e23))))) -> ((~((op2 (e20) (e20)) = (e22)))\/((op2 (e20) (e22)) = (e20))) -> (~((op2 (e20) (e20)) = (op2 (e23) (e20)))) -> ((~((op2 (e23) (e23)) = (e20)))\/((op2 (e23) (e20)) = (e23))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e21)))) -> ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((~((op1 (e11) (e11)) = (e10)))\/((op1 (e11) (e10)) = (e11))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e11)))) -> (~((op1 (e10) (e11)) = (op1 (e11) (e11)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e11) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e11) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e10))\/(((op1 (e12) (e11)) = (e10))\/((op1 (e13) (e11)) = (e10))))) -> ((~((op1 (e10) (e10)) = (e11)))\/((op1 (e10) (e11)) = (e10))) -> ((~((op1 (e11) (e11)) = (e11)))\/((op1 (e11) (e11)) = (e11))) -> (((op1 (e10) (e10)) = (e11))\/(((op1 (e10) (e11)) = (e11))\/(((op1 (e10) (e12)) = (e11))\/((op1 (e10) (e13)) = (e11))))) -> (~((op1 (e10) (e13)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e13)))) -> (((op1 (e10) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/((op1 (e13) (e11)) = (e11))))) -> (~((op1 (e11) (e10)) = (op1 (e12) (e10)))) -> (~((op1 (e10) (e11)) = (op1 (e12) (e11)))) -> (~((op1 (e12) (e13)) = (op1 (e13) (e13)))) -> (((op1 (e12) (e10)) = (e11))\/(((op1 (e12) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e11))\/((op1 (e12) (e13)) = (e11))))) -> (~((op1 (e12) (e11)) = (op1 (e12) (e12)))) -> ((~((op1 (e12) (e12)) = (e11)))\/((op1 (e12) (e11)) = (e12))) -> (~((e11) = (e13))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e12) (e12)) = (e12))\/((op1 (e13) (e13)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e10)))\/((op1 (e13) (e10)) = (e13))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (~((op2 (e21) (e20)) = (op2 (e23) (e20)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e22) (e20)) = (op2 (e23) (e20)))) -> (((op2 (e22) (e20)) = (e20))\/(((op2 (e22) (e21)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e22) (e23)) = (e20))))) -> (~((op1 (e10) (e10)) = (op1 (e10) (e13)))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e13)))) -> (~((h4 (op1 (e12) (e13))) = (op2 (h4 (e12)) (h4 (e13))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e11) (e13)) = (e10))\/(((op1 (e12) (e13)) = (e10))\/((op1 (e13) (e13)) = (e10))))) -> (~((op2 (e21) (e21)) = (op2 (e22) (e21)))) -> (((op2 (e23) (e20)) = (e20))\/(((op2 (e23) (e21)) = (e20))\/(((op2 (e23) (e22)) = (e20))\/((op2 (e23) (e23)) = (e20))))) -> (~((op2 (e20) (e22)) = (op2 (e23) (e22)))) -> ((e21) = (op2 (e23) (e23))) -> (~((op2 (e21) (e21)) = (op2 (e23) (e21)))) -> (~((op2 (e21) (e21)) = (op2 (e21) (e22)))) -> (((op2 (e20) (e22)) = (e20))\/(((op2 (e21) (e22)) = (e20))\/(((op2 (e22) (e22)) = (e20))\/((op2 (e23) (e22)) = (e20))))) -> (((op2 (e20) (e20)) = (e22))\/(((op2 (e21) (e20)) = (e22))\/(((op2 (e22) (e20)) = (e22))\/((op2 (e23) (e20)) = (e22))))) -> ((~((op1 (e10) (e10)) = (e10)))\/((op1 (e10) (e10)) = (e10))) -> ((~((op1 (e11) (e11)) = (e13)))\/((op1 (e11) (e13)) = (e11))) -> (~((op1 (e11) (e13)) = (op1 (e13) (e13)))) -> ((~((op1 (e13) (e13)) = (e13)))\/((op1 (e13) (e13)) = (e13))) -> (((op1 (e11) (e11)) = (e10))\/(((op1 (e11) (e11)) = (e11))\/(((op1 (e11) (e11)) = (e12))\/((op1 (e11) (e11)) = (e13))))) -> (~((op1 (e10) (e12)) = (op1 (e13) (e12)))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (((op1 (e11) (e10)) = (e12))\/(((op1 (e11) (e11)) = (e12))\/(((op1 (e11) (e12)) = (e12))\/((op1 (e11) (e13)) = (e12))))) -> (((op1 (e10) (e13)) = (e13))\/(((op1 (e11) (e13)) = (e13))\/(((op1 (e12) (e13)) = (e13))\/((op1 (e13) (e13)) = (e13))))) -> (~((e12) = (e13))) -> (~((e10) = (e13))) -> (((op1 (e11) (e10)) = (e13))\/(((op1 (e11) (e11)) = (e13))\/(((op1 (e11) (e12)) = (e13))\/((op1 (e11) (e13)) = (e13))))) -> (~((op1 (e11) (e12)) = (op1 (e12) (e12)))) -> (~((op1 (e11) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e10) (e11)) = (e10))\/(((op1 (e10) (e12)) = (e10))\/((op1 (e10) (e13)) = (e10))))) -> (~((op1 (e11) (e10)) = (op1 (e11) (e12)))) -> ((~((op1 (e11) (e11)) = (e12)))\/((op1 (e11) (e12)) = (e11))) -> (((op1 (e10) (e13)) = (e10))\/(((op1 (e10) (e13)) = (e11))\/(((op1 (e10) (e13)) = (e12))\/((op1 (e10) (e13)) = (e13))))) -> (~((op1 (e10) (e13)) = (op1 (e11) (e13)))) -> (~((op1 (e10) (e11)) = (op1 (e13) (e11)))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e11) (e10)) = (e13))\/(((op1 (e12) (e10)) = (e13))\/((op1 (e13) (e10)) = (e13))))) -> (((op1 (e10) (e10)) = (e13))\/(((op1 (e10) (e11)) = (e13))\/(((op1 (e10) (e12)) = (e13))\/((op1 (e10) (e13)) = (e13))))) -> ((~((op1 (e10) (e10)) = (e13)))\/((op1 (e10) (e13)) = (e10))) -> ((~((op1 (e12) (e12)) = (e10)))\/((op1 (e12) (e10)) = (e12))) -> (~((op1 (e12) (e10)) = (op1 (e13) (e10)))) -> (((op1 (e10) (e10)) = (e10))\/(((op1 (e11) (e10)) = (e10))\/(((op1 (e12) (e10)) = (e10))\/((op1 (e13) (e10)) = (e10))))) -> (((op1 (e10) (e12)) = (e10))\/(((op1 (e11) (e12)) = (e10))\/(((op1 (e12) (e12)) = (e10))\/((op1 (e13) (e12)) = (e10))))) -> (~((op1 (e11) (e11)) = (op1 (e11) (e12)))) -> (((~((op1 (e10) (op1 (e10) (e10))) = (op1 (e10) (e10))))/\((~((op1 (e11) (op1 (e10) (e11))) = (op1 (e10) (e11))))/\((~((op1 (e12) (op1 (e10) (e12))) = (op1 (e10) (e12))))/\(~((op1 (e13) (op1 (e10) (e13))) = (op1 (e10) (e13)))))))\/(((~((op1 (e10) (op1 (e11) (e10))) = (op1 (e11) (e10))))/\((~((op1 (e11) (op1 (e11) (e11))) = (op1 (e11) (e11))))/\((~((op1 (e12) (op1 (e11) (e12))) = (op1 (e11) (e12))))/\(~((op1 (e13) (op1 (e11) (e13))) = (op1 (e11) (e13)))))))\/(((~((op1 (e10) (op1 (e12) (e10))) = (op1 (e12) (e10))))/\((~((op1 (e11) (op1 (e12) (e11))) = (op1 (e12) (e11))))/\((~((op1 (e12) (op1 (e12) (e12))) = (op1 (e12) (e12))))/\(~((op1 (e13) (op1 (e12) (e13))) = (op1 (e12) (e13)))))))\/((~((op1 (e10) (op1 (e13) (e10))) = (op1 (e13) (e10))))/\((~((op1 (e11) (op1 (e13) (e11))) = (op1 (e13) (e11))))/\((~((op1 (e12) (op1 (e13) (e12))) = (op1 (e13) (e12))))/\(~((op1 (e13) (op1 (e13) (e13))) = (op1 (e13) (e13)))))))))) -> ((~((op2 (e22) (e22)) = (e20)))\/((op2 (e22) (e20)) = (e22))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H2a4 zenon_H6f zenon_H70 zenon_H71 zenon_H62 zenon_H5e zenon_H73 zenon_H40 zenon_H4a zenon_H4e zenon_H54 zenon_H6a zenon_H74 zenon_H2a5 zenon_H248 zenon_H240 zenon_H246 zenon_H210 zenon_H209 zenon_H5a zenon_H20b zenon_H1ec zenon_H22e zenon_H220 zenon_H21c zenon_H22c zenon_H245 zenon_H23a zenon_H243 zenon_H83 zenon_H38 zenon_H33 zenon_H19 zenon_H2e zenon_H24b zenon_H2be zenon_H3a6 zenon_H3a9 zenon_H87 zenon_H279 zenon_H1dc zenon_H244 zenon_H234 zenon_H239 zenon_Hb1 zenon_Hac zenon_H92 zenon_H93 zenon_H90 zenon_H9a zenon_Ha1 zenon_Ha7 zenon_He4 zenon_He5 zenon_He6 zenon_Hd7 zenon_Hd3 zenon_He8 zenon_Hb9 zenon_Hc3 zenon_Hc7 zenon_Hcd zenon_Hdf zenon_He9 zenon_Hf9 zenon_Hfd zenon_H3a5 zenon_H186 zenon_H172 zenon_H1e3 zenon_H1dd zenon_H1a zenon_H1e7 zenon_H29f zenon_H195 zenon_H2e9 zenon_H399 zenon_H108 zenon_H334 zenon_H2fe zenon_H3a0 zenon_H21 zenon_H201 zenon_H1fd zenon_H17 zenon_H28 zenon_H28b zenon_H297 zenon_H211 zenon_H1cb zenon_H175 zenon_H168 zenon_H174 zenon_H139 zenon_H132 zenon_H11d zenon_H128 zenon_H126 zenon_H12c zenon_H130 zenon_H15f zenon_H161 zenon_H153 zenon_H14e zenon_H160 zenon_H145 zenon_H140 zenon_H173 zenon_H16e zenon_H171 zenon_H1a0 zenon_H198 zenon_H179 zenon_H18a zenon_H19f zenon_H19e zenon_H1c3 zenon_H1bf zenon_H1c4 zenon_H1b6 zenon_H1a9 zenon_H1ca zenon_H247. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H86). zenon_intro zenon_H13. zenon_intro zenon_H88. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H88). zenon_intro zenon_H8a. zenon_intro zenon_H89. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H89). zenon_intro zenon_H72. zenon_intro zenon_H8b. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_L267_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_L21_); trivial. % 33.05/33.22 apply (zenon_L23_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H223. zenon_intro zenon_H2ad. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_L267_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a5); [ zenon_intro zenon_H15 | zenon_intro zenon_H14 ]. % 33.05/33.22 apply (zenon_L112_); trivial. % 33.05/33.22 apply (zenon_L267_); trivial. % 33.05/33.22 apply (zenon_L23_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H27f). zenon_intro zenon_H26c. zenon_intro zenon_H280. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H280). zenon_intro zenon_H255. zenon_intro zenon_H281. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H281). zenon_intro zenon_H27d. zenon_intro zenon_H282. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.22 apply (zenon_L267_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.22 apply (zenon_L9_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.22 apply (zenon_L126_); trivial. % 33.05/33.22 apply (zenon_L23_); trivial. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H279); [ zenon_intro zenon_H1e2 | zenon_intro zenon_H1fe ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H247); [ zenon_intro zenon_H1fa | zenon_intro zenon_H1e8 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H244); [ zenon_intro zenon_H202 | zenon_intro zenon_H235 ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1ca); [ zenon_intro zenon_Hfc | zenon_intro zenon_H1cc ]. % 33.05/33.22 apply (zenon_L46_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cc); [ zenon_intro zenon_H1ce | zenon_intro zenon_H1cd ]. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1ce). zenon_intro zenon_H1d0. zenon_intro zenon_H1cf. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1cf). zenon_intro zenon_H1d2. zenon_intro zenon_H1d1. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d1). zenon_intro zenon_H156. zenon_intro zenon_H1d3. % 33.05/33.22 apply (zenon_or_s _ _ zenon_Hfd); [ zenon_intro zenon_H104 | zenon_intro zenon_H103 ]. % 33.05/33.22 apply (zenon_L268_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H103); [ zenon_intro zenon_Hae | zenon_intro zenon_H106 ]. % 33.05/33.22 apply (zenon_L32_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H106); [ zenon_intro zenon_Hdd | zenon_intro zenon_Hfa ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.05/33.22 apply (zenon_L66_); trivial. % 33.05/33.22 apply (zenon_L268_); trivial. % 33.05/33.22 apply (zenon_L45_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cd); [ zenon_intro zenon_H19d | zenon_intro zenon_H1d4 ]. % 33.05/33.22 apply (zenon_L77_); trivial. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d4). zenon_intro zenon_H1d6. zenon_intro zenon_H1d5. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d5). zenon_intro zenon_H1d8. zenon_intro zenon_H1d7. % 33.05/33.22 apply (zenon_and_s _ _ zenon_H1d7). zenon_intro zenon_H1af. zenon_intro zenon_H1d9. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H1cb); [ zenon_intro zenon_H105 | zenon_intro zenon_H104 ]. % 33.05/33.22 apply (zenon_L85_); trivial. % 33.05/33.22 apply (zenon_L268_); trivial. % 33.05/33.22 apply (zenon_L109_); trivial. % 33.05/33.22 apply (zenon_L91_); trivial. % 33.05/33.22 apply (zenon_L137_); trivial. % 33.05/33.22 (* end of lemma zenon_L269_ *) % 33.05/33.22 assert (zenon_L270_ : (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op1 (e13) (e10)) = (e12)) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> False). % 33.05/33.22 do 0 intro. intros zenon_H3ac zenon_H2fe zenon_H2d7 zenon_H108 zenon_H334. % 33.05/33.22 cut (((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3ac. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H2fe. % 33.05/33.22 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (h4 (e13)) (h4 (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3ad]. % 33.05/33.22 cut (((h4 (e12)) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3ae]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [ zenon_intro zenon_H3af | zenon_intro zenon_H3b0 ]. % 33.05/33.22 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10)))) = ((h4 (e12)) = (h4 (op1 (e13) (e10))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3ae. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H3af. % 33.05/33.22 cut (((h4 (op1 (e13) (e10))) = (h4 (op1 (e13) (e10))))); [idtac | apply NNPP; zenon_intro zenon_H3b0]. % 33.05/33.22 cut (((h4 (op1 (e13) (e10))) = (h4 (e12)))); [idtac | apply NNPP; zenon_intro zenon_H3b1]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((op1 (e13) (e10)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H319]. % 33.05/33.22 congruence. % 33.05/33.22 exact (zenon_H319 zenon_H2d7). % 33.05/33.22 apply zenon_H3b0. apply refl_equal. % 33.05/33.22 apply zenon_H3b0. apply refl_equal. % 33.05/33.22 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3b2]. % 33.05/33.22 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3b3]. % 33.05/33.22 congruence. % 33.05/33.22 apply zenon_H3b3. apply sym_equal. exact zenon_H334. % 33.05/33.22 apply zenon_H3b2. apply sym_equal. exact zenon_H108. % 33.05/33.22 (* end of lemma zenon_L270_ *) % 33.05/33.22 assert (zenon_L271_ : ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((op1 (e13) (e11)) = (e12)) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H126 zenon_H3b4 zenon_H93 zenon_H186. % 33.05/33.22 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 33.05/33.22 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((op1 (e13) (e10)) = (op1 (e13) (e11)))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H186. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_Ha2. % 33.05/33.22 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 33.05/33.22 cut (((op1 (e13) (e11)) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3b5]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) = ((op1 (e13) (e11)) = (op1 (e13) (e10)))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3b5. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H126. % 33.05/33.22 cut (((op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) = (op1 (e13) (e10)))); [idtac | apply NNPP; zenon_intro zenon_H124]. % 33.05/33.22 cut (((e12) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3b6]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((op1 (e13) (e11)) = (op1 (e13) (e11)))); [ zenon_intro zenon_Ha2 | zenon_intro zenon_Ha3 ]. % 33.05/33.22 cut (((op1 (e13) (e11)) = (op1 (e13) (e11))) = ((e12) = (op1 (e13) (e11)))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3b6. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_Ha2. % 33.05/33.22 cut (((op1 (e13) (e11)) = (op1 (e13) (e11)))); [idtac | apply NNPP; zenon_intro zenon_Ha3]. % 33.05/33.22 cut (((op1 (e13) (e11)) = (e12))); [idtac | apply NNPP; zenon_intro zenon_H3b7]. % 33.05/33.22 congruence. % 33.05/33.22 exact (zenon_H3b7 zenon_H3b4). % 33.05/33.22 apply zenon_Ha3. apply refl_equal. % 33.05/33.22 apply zenon_Ha3. apply refl_equal. % 33.05/33.22 apply (zenon_L52_); trivial. % 33.05/33.22 apply zenon_Ha3. apply refl_equal. % 33.05/33.22 apply zenon_Ha3. apply refl_equal. % 33.05/33.22 (* end of lemma zenon_L271_ *) % 33.05/33.22 assert (zenon_L272_ : ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> (((op1 (e13) (e10)) = (e12))\/(((op1 (e13) (e11)) = (e12))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e13)) = (e12))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e11)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((h4 (op1 (e13) (e10))) = (op2 (h4 (e13)) (h4 (e10))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((~((op1 (e13) (e13)) = (e12)))\/((op1 (e13) (e12)) = (e13))) -> ((e11) = (op1 (e13) (e13))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H172 zenon_H3b8 zenon_H128 zenon_H93 zenon_H126 zenon_H186 zenon_H108 zenon_H334 zenon_H2fe zenon_H3ac zenon_H12c zenon_H3b9 zenon_H90. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.05/33.22 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3b9); [ zenon_intro zenon_H3ba | zenon_intro zenon_H12e ]. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3b8); [ zenon_intro zenon_H2d7 | zenon_intro zenon_H3bb ]. % 33.05/33.22 apply (zenon_L270_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3bb); [ zenon_intro zenon_H3b4 | zenon_intro zenon_H3bc ]. % 33.05/33.22 apply (zenon_L271_); trivial. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H3bc); [ zenon_intro zenon_H127 | zenon_intro zenon_H3bd ]. % 33.05/33.22 apply (zenon_L53_); trivial. % 33.05/33.22 exact (zenon_H3ba zenon_H3bd). % 33.05/33.22 apply (zenon_L54_); trivial. % 33.05/33.22 (* end of lemma zenon_L272_ *) % 33.05/33.22 assert (zenon_L273_ : ((h4 (e13)) = (e23)) -> ((op1 (e13) (e11)) = (e13)) -> (~((e23) = (h4 (op1 (e13) (e11))))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H334 zenon_H12d zenon_H3be. % 33.05/33.22 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H3bf | zenon_intro zenon_H3c0 ]. % 33.05/33.22 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((e23) = (h4 (op1 (e13) (e11))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3be. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H3bf. % 33.05/33.22 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c0]. % 33.05/33.22 cut (((h4 (op1 (e13) (e11))) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H3c1]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((h4 (e13)) = (e23)) = ((h4 (op1 (e13) (e11))) = (e23))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3c1. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H334. % 33.05/33.22 cut (((e23) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H1da]. % 33.05/33.22 cut (((h4 (e13)) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c2]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [ zenon_intro zenon_H3bf | zenon_intro zenon_H3c0 ]. % 33.05/33.22 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11)))) = ((h4 (e13)) = (h4 (op1 (e13) (e11))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3c2. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H3bf. % 33.05/33.22 cut (((h4 (op1 (e13) (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c0]. % 33.05/33.22 cut (((h4 (op1 (e13) (e11))) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3c3]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((op1 (e13) (e11)) = (e13))); [idtac | apply NNPP; zenon_intro zenon_H31b]. % 33.05/33.22 congruence. % 33.05/33.22 exact (zenon_H31b zenon_H12d). % 33.05/33.22 apply zenon_H3c0. apply refl_equal. % 33.05/33.22 apply zenon_H3c0. apply refl_equal. % 33.05/33.22 apply zenon_H1da. apply refl_equal. % 33.05/33.22 apply zenon_H3c0. apply refl_equal. % 33.05/33.22 apply zenon_H3c0. apply refl_equal. % 33.05/33.22 (* end of lemma zenon_L273_ *) % 33.05/33.22 assert (zenon_L274_ : ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((e11) = (op1 (e13) (e13))) -> (~((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))) -> ((h4 (e13)) = (e23)) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.05/33.22 do 0 intro. intros zenon_H239 zenon_H90 zenon_H3c4 zenon_H334 zenon_H2fb zenon_H172 zenon_H17. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H18 | zenon_intro zenon_H236 ]. % 33.05/33.22 apply zenon_H18. apply sym_equal. exact zenon_H17. % 33.05/33.22 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.05/33.22 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.22 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H3c5 | zenon_intro zenon_H3c6 ]. % 33.05/33.22 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((h4 (op1 (e13) (e11))) = (op2 (h4 (e13)) (h4 (e11))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3c4. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H3c5. % 33.05/33.22 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c6]. % 33.05/33.22 cut (((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c7]. % 33.05/33.22 congruence. % 33.05/33.22 cut (((op2 (e23) (e21)) = (e23)) = ((op2 (h4 (e13)) (h4 (e11))) = (h4 (op1 (e13) (e11))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3c7. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H236. % 33.05/33.22 cut (((e23) = (h4 (op1 (e13) (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3be]. % 33.05/33.22 cut (((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c8]. % 33.05/33.22 congruence. % 33.05/33.22 elim (classic ((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [ zenon_intro zenon_H3c5 | zenon_intro zenon_H3c6 ]. % 33.05/33.22 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11)))) = ((op2 (e23) (e21)) = (op2 (h4 (e13)) (h4 (e11))))). % 33.05/33.22 intro zenon_D_pnotp. % 33.05/33.22 apply zenon_H3c8. % 33.05/33.22 rewrite <- zenon_D_pnotp. % 33.05/33.22 exact zenon_H3c5. % 33.05/33.22 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (h4 (e13)) (h4 (e11))))); [idtac | apply NNPP; zenon_intro zenon_H3c6]. % 33.05/33.23 cut (((op2 (h4 (e13)) (h4 (e11))) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H3c9]. % 33.05/33.23 congruence. % 33.05/33.23 cut (((h4 (e11)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H2fa]. % 33.05/33.23 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 33.05/33.23 congruence. % 33.05/33.23 exact (zenon_H340 zenon_H334). % 33.05/33.23 apply (zenon_L166_); trivial. % 33.05/33.23 apply zenon_H3c6. apply refl_equal. % 33.05/33.23 apply zenon_H3c6. apply refl_equal. % 33.05/33.23 apply (zenon_L273_); trivial. % 33.05/33.23 apply zenon_H3c6. apply refl_equal. % 33.05/33.23 apply zenon_H3c6. apply refl_equal. % 33.05/33.23 (* end of lemma zenon_L274_ *) % 33.05/33.23 assert (zenon_L275_ : ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op1 (e13) (e12)) = (e10)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((e20) = (h4 (op1 (e13) (e12))))) -> False). % 33.05/33.23 do 0 intro. intros zenon_H108 zenon_H118 zenon_H1a zenon_H3ca. % 33.05/33.23 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H3cb | zenon_intro zenon_H3cc ]. % 33.05/33.23 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((e20) = (h4 (op1 (e13) (e12))))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3ca. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3cb. % 33.05/33.23 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3cc]. % 33.05/33.23 cut (((h4 (op1 (e13) (e12))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H3cd]. % 33.05/33.23 congruence. % 33.05/33.23 cut (((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = ((h4 (op1 (e13) (e12))) = (e20))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3cd. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H108. % 33.05/33.23 cut (((op2 (op2 (e23) (e23)) (op2 (e23) (e23))) = (e20))); [idtac | apply NNPP; zenon_intro zenon_H109]. % 33.05/33.23 cut (((h4 (e10)) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3ce]. % 33.05/33.23 congruence. % 33.05/33.23 elim (classic ((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [ zenon_intro zenon_H3cb | zenon_intro zenon_H3cc ]. % 33.05/33.23 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12)))) = ((h4 (e10)) = (h4 (op1 (e13) (e12))))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3ce. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3cb. % 33.05/33.23 cut (((h4 (op1 (e13) (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3cc]. % 33.05/33.23 cut (((h4 (op1 (e13) (e12))) = (h4 (e10)))); [idtac | apply NNPP; zenon_intro zenon_H3cf]. % 33.05/33.23 congruence. % 33.05/33.23 cut (((op1 (e13) (e12)) = (e10))); [idtac | apply NNPP; zenon_intro zenon_H1b5]. % 33.05/33.23 congruence. % 33.05/33.23 exact (zenon_H1b5 zenon_H118). % 33.05/33.23 apply zenon_H3cc. apply refl_equal. % 33.05/33.23 apply zenon_H3cc. apply refl_equal. % 33.05/33.23 apply zenon_H109. apply sym_equal. exact zenon_H1a. % 33.05/33.23 apply zenon_H3cc. apply refl_equal. % 33.05/33.23 apply zenon_H3cc. apply refl_equal. % 33.05/33.23 (* end of lemma zenon_L275_ *) % 33.05/33.23 assert (zenon_L276_ : ((op2 (e23) (e22)) = (e20)) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((op1 (e13) (e12)) = (e10)) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> False). % 33.05/33.23 do 0 intro. intros zenon_H1ff zenon_H334 zenon_H2fe zenon_H1dd zenon_H108 zenon_H1a zenon_H118 zenon_H3d0. % 33.05/33.23 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3d2 ]. % 33.05/33.23 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3d0. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3d1. % 33.05/33.23 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3d2]. % 33.05/33.23 cut (((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3d3]. % 33.05/33.23 congruence. % 33.05/33.23 cut (((op2 (e23) (e22)) = (e20)) = ((op2 (h4 (e13)) (h4 (e12))) = (h4 (op1 (e13) (e12))))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3d3. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H1ff. % 33.05/33.23 cut (((e20) = (h4 (op1 (e13) (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3ca]. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3d4]. % 33.05/33.23 congruence. % 33.05/33.23 elim (classic ((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [ zenon_intro zenon_H3d1 | zenon_intro zenon_H3d2 ]. % 33.05/33.23 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12)))) = ((op2 (e23) (e22)) = (op2 (h4 (e13)) (h4 (e12))))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3d4. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3d1. % 33.05/33.23 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (h4 (e13)) (h4 (e12))))); [idtac | apply NNPP; zenon_intro zenon_H3d2]. % 33.05/33.23 cut (((op2 (h4 (e13)) (h4 (e12))) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3d5]. % 33.05/33.23 congruence. % 33.05/33.23 cut (((h4 (e12)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H325]. % 33.05/33.23 cut (((h4 (e13)) = (e23))); [idtac | apply NNPP; zenon_intro zenon_H340]. % 33.05/33.23 congruence. % 33.05/33.23 exact (zenon_H340 zenon_H334). % 33.05/33.23 apply (zenon_L202_); trivial. % 33.05/33.23 apply zenon_H3d2. apply refl_equal. % 33.05/33.23 apply zenon_H3d2. apply refl_equal. % 33.05/33.23 apply (zenon_L275_); trivial. % 33.05/33.23 apply zenon_H3d2. apply refl_equal. % 33.05/33.23 apply zenon_H3d2. apply refl_equal. % 33.05/33.23 (* end of lemma zenon_L276_ *) % 33.05/33.23 assert (zenon_L277_ : (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((h4 (e13)) = (e23)) -> ((op2 (e23) (e22)) = (e20)) -> ((e11) = (op1 (e13) (e13))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> ((op1 (e13) (e11)) = (e13)) -> False). % 33.05/33.23 do 0 intro. intros zenon_H130 zenon_H3d0 zenon_H1a zenon_H108 zenon_H1dd zenon_H2fe zenon_H334 zenon_H1ff zenon_H90 zenon_H11d zenon_H128 zenon_H93 zenon_H126 zenon_H12c zenon_H12d. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H130); [ zenon_intro zenon_H118 | zenon_intro zenon_H133 ]. % 33.05/33.23 apply (zenon_L276_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H133); [ zenon_intro zenon_H11e | zenon_intro zenon_H138 ]. % 33.05/33.23 apply (zenon_L50_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H138); [ zenon_intro zenon_H127 | zenon_intro zenon_H12e ]. % 33.05/33.23 apply (zenon_L53_); trivial. % 33.05/33.23 apply (zenon_L54_); trivial. % 33.05/33.23 (* end of lemma zenon_L277_ *) % 33.05/33.23 assert (zenon_L278_ : (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> ((e21) = (op2 (e23) (e23))) -> ((op2 (e23) (e22)) = (e21)) -> False). % 33.05/33.23 do 0 intro. intros zenon_H3d6 zenon_H17 zenon_H3d7. % 33.05/33.23 cut (((e21) = (op2 (e23) (e23))) = ((op2 (e23) (e22)) = (op2 (e23) (e23)))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3d6. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H17. % 33.05/33.23 cut (((op2 (e23) (e23)) = (op2 (e23) (e23)))); [idtac | apply NNPP; zenon_intro zenon_H3c]. % 33.05/33.23 cut (((e21) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3d8]. % 33.05/33.23 congruence. % 33.05/33.23 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H3d9 | zenon_intro zenon_H3da ]. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e21) = (op2 (e23) (e22)))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3d8. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3d9. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3da]. % 33.05/33.23 cut (((op2 (e23) (e22)) = (e21))); [idtac | apply NNPP; zenon_intro zenon_H3db]. % 33.05/33.23 congruence. % 33.05/33.23 exact (zenon_H3db zenon_H3d7). % 33.05/33.23 apply zenon_H3da. apply refl_equal. % 33.05/33.23 apply zenon_H3da. apply refl_equal. % 33.05/33.23 apply zenon_H3c. apply refl_equal. % 33.05/33.23 (* end of lemma zenon_L278_ *) % 33.05/33.23 assert (zenon_L279_ : ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((op2 (e23) (e22)) = (e22)) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> False). % 33.05/33.23 do 0 intro. intros zenon_H1dd zenon_H3dc zenon_H1a zenon_H3dd. % 33.05/33.23 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H3d9 | zenon_intro zenon_H3da ]. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((op2 (e23) (e20)) = (op2 (e23) (e22)))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3dd. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3d9. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3da]. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H3de]. % 33.05/33.23 congruence. % 33.05/33.23 cut (((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) = ((op2 (e23) (e22)) = (op2 (e23) (e20)))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3de. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H1dd. % 33.05/33.23 cut (((op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) = (op2 (e23) (e20)))); [idtac | apply NNPP; zenon_intro zenon_H1db]. % 33.05/33.23 cut (((e22) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3df]. % 33.05/33.23 congruence. % 33.05/33.23 elim (classic ((op2 (e23) (e22)) = (op2 (e23) (e22)))); [ zenon_intro zenon_H3d9 | zenon_intro zenon_H3da ]. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (e23) (e22))) = ((e22) = (op2 (e23) (e22)))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3df. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3d9. % 33.05/33.23 cut (((op2 (e23) (e22)) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3da]. % 33.05/33.23 cut (((op2 (e23) (e22)) = (e22))); [idtac | apply NNPP; zenon_intro zenon_H3e0]. % 33.05/33.23 congruence. % 33.05/33.23 exact (zenon_H3e0 zenon_H3dc). % 33.05/33.23 apply zenon_H3da. apply refl_equal. % 33.05/33.23 apply zenon_H3da. apply refl_equal. % 33.05/33.23 apply (zenon_L88_); trivial. % 33.05/33.23 apply zenon_H3da. apply refl_equal. % 33.05/33.23 apply zenon_H3da. apply refl_equal. % 33.05/33.23 (* end of lemma zenon_L279_ *) % 33.05/33.23 assert (zenon_L280_ : (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> ((op2 (e23) (e21)) = (e23)) -> ((op2 (e23) (e22)) = (e23)) -> False). % 33.05/33.23 do 0 intro. intros zenon_H3e1 zenon_H236 zenon_H3e2. % 33.05/33.23 cut (((op2 (e23) (e21)) = (e23)) = ((op2 (e23) (e21)) = (op2 (e23) (e22)))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3e1. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H236. % 33.05/33.23 cut (((e23) = (op2 (e23) (e22)))); [idtac | apply NNPP; zenon_intro zenon_H3e3]. % 33.05/33.23 cut (((op2 (e23) (e21)) = (op2 (e23) (e21)))); [idtac | apply NNPP; zenon_intro zenon_H2a]. % 33.05/33.23 congruence. % 33.05/33.23 apply zenon_H2a. apply refl_equal. % 33.05/33.23 apply zenon_H3e3. apply sym_equal. exact zenon_H3e2. % 33.05/33.23 (* end of lemma zenon_L280_ *) % 33.05/33.23 assert (zenon_L281_ : ((~((op2 (e23) (e23)) = (e21)))\/((op2 (e23) (e21)) = (e23))) -> ((e11) = (op1 (e13) (e13))) -> (((op2 (e23) (e22)) = (e20))\/(((op2 (e23) (e22)) = (e21))\/(((op2 (e23) (e22)) = (e22))\/((op2 (e23) (e22)) = (e23))))) -> (~((op2 (e23) (e21)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e20)) = (op2 (e23) (e22)))) -> (~((op2 (e23) (e22)) = (op2 (e23) (e23)))) -> (~((h4 (op1 (e13) (e12))) = (op2 (h4 (e13)) (h4 (e12))))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((h4 (e13)) = (e23)) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> (~((op1 (e13) (e12)) = (op1 (e13) (e13)))) -> (~((op1 (e13) (e10)) = (op1 (e13) (e12)))) -> ((e12) = (op1 (e13) (op1 (op1 (e13) (e13)) (op1 (e13) (e13))))) -> ((e10) = (op1 (op1 (e13) (e13)) (op1 (e13) (e13)))) -> (~((op1 (e13) (e11)) = (op1 (e13) (e12)))) -> (((op1 (e13) (e12)) = (e10))\/(((op1 (e13) (e12)) = (e11))\/(((op1 (e13) (e12)) = (e12))\/((op1 (e13) (e12)) = (e13))))) -> ((~((op1 (e13) (e13)) = (e11)))\/((op1 (e13) (e11)) = (e13))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.05/33.23 do 0 intro. intros zenon_H239 zenon_H90 zenon_H3e4 zenon_H3e1 zenon_H3dd zenon_H3d6 zenon_H3d0 zenon_H1a zenon_H108 zenon_H334 zenon_H2fe zenon_H1dd zenon_H11d zenon_H128 zenon_H126 zenon_H93 zenon_H12c zenon_H130 zenon_H172 zenon_H17. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H239); [ zenon_intro zenon_H18 | zenon_intro zenon_H236 ]. % 33.05/33.23 apply zenon_H18. apply sym_equal. exact zenon_H17. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H172); [ zenon_intro zenon_H91 | zenon_intro zenon_H12d ]. % 33.05/33.23 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H3e4); [ zenon_intro zenon_H1ff | zenon_intro zenon_H3e5 ]. % 33.05/33.23 apply (zenon_L277_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H3e5); [ zenon_intro zenon_H3d7 | zenon_intro zenon_H3e6 ]. % 33.05/33.23 apply (zenon_L278_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H3e6); [ zenon_intro zenon_H3dc | zenon_intro zenon_H3e2 ]. % 33.05/33.23 apply (zenon_L279_); trivial. % 33.05/33.23 apply (zenon_L280_); trivial. % 33.05/33.23 (* end of lemma zenon_L281_ *) % 33.05/33.23 assert (zenon_L282_ : (~((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e11) = (op1 (e13) (e13))) -> ((h4 (e13)) = (e23)) -> False). % 33.05/33.23 do 0 intro. intros zenon_H3e7 zenon_H2fb zenon_H90 zenon_H334. % 33.05/33.23 cut (((h4 (e11)) = (op2 (e23) (e23))) = ((h4 (op1 (e13) (e13))) = (op2 (h4 (e13)) (h4 (e13))))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3e7. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H2fb. % 33.05/33.23 cut (((op2 (e23) (e23)) = (op2 (h4 (e13)) (h4 (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3e8]. % 33.05/33.23 cut (((h4 (e11)) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3e9]. % 33.05/33.23 congruence. % 33.05/33.23 elim (classic ((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [ zenon_intro zenon_H3ea | zenon_intro zenon_H3eb ]. % 33.05/33.23 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13)))) = ((h4 (e11)) = (h4 (op1 (e13) (e13))))). % 33.05/33.23 intro zenon_D_pnotp. % 33.05/33.23 apply zenon_H3e9. % 33.05/33.23 rewrite <- zenon_D_pnotp. % 33.05/33.23 exact zenon_H3ea. % 33.05/33.23 cut (((h4 (op1 (e13) (e13))) = (h4 (op1 (e13) (e13))))); [idtac | apply NNPP; zenon_intro zenon_H3eb]. % 33.05/33.23 cut (((h4 (op1 (e13) (e13))) = (h4 (e11)))); [idtac | apply NNPP; zenon_intro zenon_H3ec]. % 33.05/33.23 congruence. % 33.05/33.23 cut (((op1 (e13) (e13)) = (e11))); [idtac | apply NNPP; zenon_intro zenon_H91]. % 33.05/33.23 congruence. % 33.05/33.23 apply zenon_H91. apply sym_equal. exact zenon_H90. % 33.05/33.23 apply zenon_H3eb. apply refl_equal. % 33.05/33.23 apply zenon_H3eb. apply refl_equal. % 33.05/33.23 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3b3]. % 33.05/33.23 cut (((e23) = (h4 (e13)))); [idtac | apply NNPP; zenon_intro zenon_H3b3]. % 33.05/33.23 congruence. % 33.05/33.23 apply zenon_H3b3. apply sym_equal. exact zenon_H334. % 33.05/33.23 apply zenon_H3b3. apply sym_equal. exact zenon_H334. % 33.05/33.23 (* end of lemma zenon_L282_ *) % 33.05/33.23 assert (zenon_L283_ : (~(((h4 (e10)) = (e20))\/(((h4 (e11)) = (e20))\/(((h4 (e12)) = (e20))\/((h4 (e13)) = (e20)))))) -> ((h4 (e10)) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> ((e20) = (op2 (op2 (e23) (e23)) (op2 (e23) (e23)))) -> False). % 33.05/33.23 do 0 intro. intros zenon_H3ed zenon_H108 zenon_H1a. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3ed). zenon_intro zenon_H107. zenon_intro zenon_H3ee. % 33.05/33.23 apply (zenon_L47_); trivial. % 33.05/33.23 (* end of lemma zenon_L283_ *) % 33.05/33.23 assert (zenon_L284_ : (~(((h4 (e10)) = (e21))\/(((h4 (e11)) = (e21))\/(((h4 (e12)) = (e21))\/((h4 (e13)) = (e21)))))) -> ((h4 (e11)) = (op2 (e23) (e23))) -> ((e21) = (op2 (e23) (e23))) -> False). % 33.05/33.23 do 0 intro. intros zenon_H3ef zenon_H2fb zenon_H17. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3ef). zenon_intro zenon_H3f1. zenon_intro zenon_H3f0. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3f0). zenon_intro zenon_H2fa. zenon_intro zenon_H3f2. % 33.05/33.23 apply (zenon_L166_); trivial. % 33.05/33.23 (* end of lemma zenon_L284_ *) % 33.05/33.23 assert (zenon_L285_ : (~(((h4 (e10)) = (e22))\/(((h4 (e11)) = (e22))\/(((h4 (e12)) = (e22))\/((h4 (e13)) = (e22)))))) -> ((h4 (e12)) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> ((e22) = (op2 (e23) (op2 (op2 (e23) (e23)) (op2 (e23) (e23))))) -> False). % 33.05/33.23 do 0 intro. intros zenon_H3f3 zenon_H2fe zenon_H1dd. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3f3). zenon_intro zenon_H3f5. zenon_intro zenon_H3f4. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3f4). zenon_intro zenon_H3f7. zenon_intro zenon_H3f6. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3f6). zenon_intro zenon_H325. zenon_intro zenon_H3f8. % 33.05/33.23 apply (zenon_L202_); trivial. % 33.05/33.23 (* end of lemma zenon_L285_ *) % 33.05/33.23 assert (zenon_L286_ : (~(((h4 (e10)) = (e23))\/(((h4 (e11)) = (e23))\/(((h4 (e12)) = (e23))\/((h4 (e13)) = (e23)))))) -> ((h4 (e13)) = (e23)) -> False). % 33.05/33.23 do 0 intro. intros zenon_H3f9 zenon_H334. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3f9). zenon_intro zenon_H3fb. zenon_intro zenon_H3fa. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3fa). zenon_intro zenon_H3fd. zenon_intro zenon_H3fc. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H3fc). zenon_intro zenon_H3fe. zenon_intro zenon_H340. % 33.05/33.23 exact (zenon_H340 zenon_H334). % 33.05/33.23 (* end of lemma zenon_L286_ *) % 33.05/33.23 apply NNPP. intro zenon_G. % 33.05/33.23 apply (zenon_and_s _ _ ax1). zenon_intro zenon_H400. zenon_intro zenon_H3ff. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H3ff). zenon_intro zenon_H2de. zenon_intro zenon_H401. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H401). zenon_intro zenon_H403. zenon_intro zenon_H402. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H402). zenon_intro zenon_H1a0. zenon_intro zenon_H404. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H404). zenon_intro zenon_H406. zenon_intro zenon_H405. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H405). zenon_intro zenon_H139. zenon_intro zenon_H407. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H407). zenon_intro zenon_H409. zenon_intro zenon_H408. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H408). zenon_intro zenon_H2f4. zenon_intro zenon_H40a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H40a). zenon_intro zenon_H379. zenon_intro zenon_H40b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H40b). zenon_intro zenon_H40d. zenon_intro zenon_H40c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H40c). zenon_intro zenon_H40f. zenon_intro zenon_H40e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H40e). zenon_intro zenon_H411. zenon_intro zenon_H410. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H410). zenon_intro zenon_H413. zenon_intro zenon_H412. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H412). zenon_intro zenon_H415. zenon_intro zenon_H414. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H414). zenon_intro zenon_H130. zenon_intro zenon_H416. % 33.05/33.23 apply (zenon_and_s _ _ ax2). zenon_intro zenon_H173. zenon_intro zenon_H417. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H417). zenon_intro zenon_H1c4. zenon_intro zenon_H418. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H418). zenon_intro zenon_He6. zenon_intro zenon_H419. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H419). zenon_intro zenon_H41b. zenon_intro zenon_H41a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H41a). zenon_intro zenon_H30e. zenon_intro zenon_H41c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H41c). zenon_intro zenon_H2e1. zenon_intro zenon_H41d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H41d). zenon_intro zenon_H19f. zenon_intro zenon_H41e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H41e). zenon_intro zenon_H18a. zenon_intro zenon_H41f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H41f). zenon_intro zenon_H421. zenon_intro zenon_H420. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H420). zenon_intro zenon_Ha7. zenon_intro zenon_H422. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H422). zenon_intro zenon_H424. zenon_intro zenon_H423. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H423). zenon_intro zenon_He8. zenon_intro zenon_H425. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H425). zenon_intro zenon_H15f. zenon_intro zenon_H426. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H426). zenon_intro zenon_H428. zenon_intro zenon_H427. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H427). zenon_intro zenon_H160. zenon_intro zenon_H429. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H429). zenon_intro zenon_H42b. zenon_intro zenon_H42a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H42a). zenon_intro zenon_H3a9. zenon_intro zenon_H42c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H42c). zenon_intro zenon_H1b6. zenon_intro zenon_H42d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H42d). zenon_intro zenon_Hcd. zenon_intro zenon_H42e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H42e). zenon_intro zenon_H430. zenon_intro zenon_H42f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H42f). zenon_intro zenon_H2f7. zenon_intro zenon_H431. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H431). zenon_intro zenon_H433. zenon_intro zenon_H432. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H432). zenon_intro zenon_H435. zenon_intro zenon_H434. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H434). zenon_intro zenon_H437. zenon_intro zenon_H436. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H436). zenon_intro zenon_H439. zenon_intro zenon_H438. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H438). zenon_intro zenon_H3a0. zenon_intro zenon_H43a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H43a). zenon_intro zenon_H43c. zenon_intro zenon_H43b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H43b). zenon_intro zenon_H43e. zenon_intro zenon_H43d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H43d). zenon_intro zenon_H3b8. zenon_intro zenon_H43f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H43f). zenon_intro zenon_H441. zenon_intro zenon_H440. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H440). zenon_intro zenon_H442. zenon_intro zenon_H161. % 33.05/33.23 apply (zenon_and_s _ _ ax3). zenon_intro zenon_H444. zenon_intro zenon_H443. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H443). zenon_intro zenon_H446. zenon_intro zenon_H445. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H445). zenon_intro zenon_H448. zenon_intro zenon_H447. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H447). zenon_intro zenon_H27a. zenon_intro zenon_H449. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H449). zenon_intro zenon_H44b. zenon_intro zenon_H44a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H44a). zenon_intro zenon_H44d. zenon_intro zenon_H44c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H44c). zenon_intro zenon_H35e. zenon_intro zenon_H44e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H44e). zenon_intro zenon_H2cd. zenon_intro zenon_H44f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H44f). zenon_intro zenon_H274. zenon_intro zenon_H450. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H450). zenon_intro zenon_H452. zenon_intro zenon_H451. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H451). zenon_intro zenon_H2b8. zenon_intro zenon_H453. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H453). zenon_intro zenon_H455. zenon_intro zenon_H454. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H454). zenon_intro zenon_H457. zenon_intro zenon_H456. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H456). zenon_intro zenon_H459. zenon_intro zenon_H458. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H458). zenon_intro zenon_H3e4. zenon_intro zenon_H45a. % 33.05/33.23 apply (zenon_and_s _ _ ax4). zenon_intro zenon_H245. zenon_intro zenon_H45b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H45b). zenon_intro zenon_H45d. zenon_intro zenon_H45c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H45c). zenon_intro zenon_H71. zenon_intro zenon_H45e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H45e). zenon_intro zenon_H460. zenon_intro zenon_H45f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H45f). zenon_intro zenon_H210. zenon_intro zenon_H461. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H461). zenon_intro zenon_H211. zenon_intro zenon_H462. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H462). zenon_intro zenon_H464. zenon_intro zenon_H463. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H463). zenon_intro zenon_H466. zenon_intro zenon_H465. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H465). zenon_intro zenon_H468. zenon_intro zenon_H467. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H467). zenon_intro zenon_H2e. zenon_intro zenon_H469. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H469). zenon_intro zenon_H46b. zenon_intro zenon_H46a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H46a). zenon_intro zenon_H73. zenon_intro zenon_H46c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H46c). zenon_intro zenon_H20b. zenon_intro zenon_H46d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H46d). zenon_intro zenon_H25f. zenon_intro zenon_H46e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H46e). zenon_intro zenon_H22c. zenon_intro zenon_H46f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H46f). zenon_intro zenon_H471. zenon_intro zenon_H470. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H470). zenon_intro zenon_H29f. zenon_intro zenon_H472. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H472). zenon_intro zenon_H297. zenon_intro zenon_H473. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H473). zenon_intro zenon_H54. zenon_intro zenon_H474. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H474). zenon_intro zenon_H476. zenon_intro zenon_H475. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H475). zenon_intro zenon_H2c9. zenon_intro zenon_H477. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H477). zenon_intro zenon_H479. zenon_intro zenon_H478. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H478). zenon_intro zenon_H47b. zenon_intro zenon_H47a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H47a). zenon_intro zenon_H47d. zenon_intro zenon_H47c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H47c). zenon_intro zenon_H201. zenon_intro zenon_H47e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H47e). zenon_intro zenon_H3a6. zenon_intro zenon_H47f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H47f). zenon_intro zenon_H481. zenon_intro zenon_H480. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H480). zenon_intro zenon_H483. zenon_intro zenon_H482. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H482). zenon_intro zenon_H485. zenon_intro zenon_H484. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H484). zenon_intro zenon_H487. zenon_intro zenon_H486. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H486). zenon_intro zenon_H488. zenon_intro zenon_H22e. % 33.05/33.23 apply (zenon_and_s _ _ ax5). zenon_intro zenon_H48a. zenon_intro zenon_H489. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H489). zenon_intro zenon_H48c. zenon_intro zenon_H48b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H48b). zenon_intro zenon_H48e. zenon_intro zenon_H48d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H48d). zenon_intro zenon_Hb9. zenon_intro zenon_H48f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H48f). zenon_intro zenon_H140. zenon_intro zenon_H490. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H490). zenon_intro zenon_H1bf. zenon_intro zenon_H491. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H491). zenon_intro zenon_H92. zenon_intro zenon_H492. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H492). zenon_intro zenon_Hc3. zenon_intro zenon_H493. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H493). zenon_intro zenon_H179. zenon_intro zenon_H494. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H494). zenon_intro zenon_H9a. zenon_intro zenon_H495. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H495). zenon_intro zenon_Ha1. zenon_intro zenon_H496. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H496). zenon_intro zenon_H498. zenon_intro zenon_H497. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H497). zenon_intro zenon_H49a. zenon_intro zenon_H499. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H499). zenon_intro zenon_H2e3. zenon_intro zenon_H49b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H49b). zenon_intro zenon_H132. zenon_intro zenon_H49c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H49c). zenon_intro zenon_H145. zenon_intro zenon_H49d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H49d). zenon_intro zenon_H49f. zenon_intro zenon_H49e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H49e). zenon_intro zenon_H4a1. zenon_intro zenon_H4a0. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a0). zenon_intro zenon_H198. zenon_intro zenon_H4a2. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a2). zenon_intro zenon_H4a4. zenon_intro zenon_H4a3. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a3). zenon_intro zenon_Hd7. zenon_intro zenon_H4a5. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a5). zenon_intro zenon_H2ef. zenon_intro zenon_H4a6. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a6). zenon_intro zenon_H168. zenon_intro zenon_H4a7. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a7). zenon_intro zenon_Hc7. zenon_intro zenon_H4a8. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a8). zenon_intro zenon_H4aa. zenon_intro zenon_H4a9. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4a9). zenon_intro zenon_H311. zenon_intro zenon_H4ab. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ab). zenon_intro zenon_H195. zenon_intro zenon_H4ac. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ac). zenon_intro zenon_H4ae. zenon_intro zenon_H4ad. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ad). zenon_intro zenon_H4b0. zenon_intro zenon_H4af. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4af). zenon_intro zenon_H4b2. zenon_intro zenon_H4b1. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4b1). zenon_intro zenon_Hac. zenon_intro zenon_H4b3. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4b3). zenon_intro zenon_H16e. zenon_intro zenon_H4b4. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4b4). zenon_intro zenon_H4b6. zenon_intro zenon_H4b5. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4b5). zenon_intro zenon_H1a9. zenon_intro zenon_H4b7. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4b7). zenon_intro zenon_H2e9. zenon_intro zenon_H4b8. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4b8). zenon_intro zenon_H4ba. zenon_intro zenon_H4b9. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4b9). zenon_intro zenon_H4bc. zenon_intro zenon_H4bb. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4bb). zenon_intro zenon_H4be. zenon_intro zenon_H4bd. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4bd). zenon_intro zenon_H4c0. zenon_intro zenon_H4bf. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4bf). zenon_intro zenon_Hdf. zenon_intro zenon_H4c1. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4c1). zenon_intro zenon_H4c3. zenon_intro zenon_H4c2. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4c2). zenon_intro zenon_H4c5. zenon_intro zenon_H4c4. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4c4). zenon_intro zenon_H186. zenon_intro zenon_H4c6. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4c6). zenon_intro zenon_H128. zenon_intro zenon_H4c7. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4c7). zenon_intro zenon_H4c9. zenon_intro zenon_H4c8. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4c8). zenon_intro zenon_H12c. zenon_intro zenon_H4ca. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ca). zenon_intro zenon_Hd3. zenon_intro zenon_H11d. % 33.05/33.23 apply (zenon_and_s _ _ ax6). zenon_intro zenon_H4cc. zenon_intro zenon_H4cb. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4cb). zenon_intro zenon_H268. zenon_intro zenon_H4cd. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4cd). zenon_intro zenon_H1dc. zenon_intro zenon_H4ce. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ce). zenon_intro zenon_H40. zenon_intro zenon_H4cf. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4cf). zenon_intro zenon_H1e3. zenon_intro zenon_H4d0. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d0). zenon_intro zenon_H1e7. zenon_intro zenon_H4d1. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d1). zenon_intro zenon_H19. zenon_intro zenon_H4d2. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d2). zenon_intro zenon_H4a. zenon_intro zenon_H4d3. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d3). zenon_intro zenon_H4d5. zenon_intro zenon_H4d4. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d4). zenon_intro zenon_H21. zenon_intro zenon_H4d6. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d6). zenon_intro zenon_H28. zenon_intro zenon_H4d7. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d7). zenon_intro zenon_H4d9. zenon_intro zenon_H4d8. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4d8). zenon_intro zenon_H4db. zenon_intro zenon_H4da. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4da). zenon_intro zenon_H5a. zenon_intro zenon_H4dc. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4dc). zenon_intro zenon_H1fd. zenon_intro zenon_H4dd. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4dd). zenon_intro zenon_H1ec. zenon_intro zenon_H4de. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4de). zenon_intro zenon_H4e0. zenon_intro zenon_H4df. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4df). zenon_intro zenon_H4e2. zenon_intro zenon_H4e1. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e1). zenon_intro zenon_H209. zenon_intro zenon_H4e3. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e3). zenon_intro zenon_H29e. zenon_intro zenon_H4e4. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e4). zenon_intro zenon_H62. zenon_intro zenon_H4e5. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e5). zenon_intro zenon_H2c5. zenon_intro zenon_H4e6. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e6). zenon_intro zenon_H23a. zenon_intro zenon_H4e7. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e7). zenon_intro zenon_H4e. zenon_intro zenon_H4e8. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e8). zenon_intro zenon_H4ea. zenon_intro zenon_H4e9. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4e9). zenon_intro zenon_H277. zenon_intro zenon_H4eb. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4eb). zenon_intro zenon_H24b. zenon_intro zenon_H4ec. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ec). zenon_intro zenon_H4ee. zenon_intro zenon_H4ed. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ed). zenon_intro zenon_H251. zenon_intro zenon_H4ef. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4ef). zenon_intro zenon_H4f1. zenon_intro zenon_H4f0. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4f0). zenon_intro zenon_H33. zenon_intro zenon_H4f2. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4f2). zenon_intro zenon_H240. zenon_intro zenon_H4f3. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4f3). zenon_intro zenon_H4f5. zenon_intro zenon_H4f4. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4f4). zenon_intro zenon_H28b. zenon_intro zenon_H4f6. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4f6). zenon_intro zenon_H2be. zenon_intro zenon_H4f7. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4f7). zenon_intro zenon_H4f9. zenon_intro zenon_H4f8. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4f8). zenon_intro zenon_H4fb. zenon_intro zenon_H4fa. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4fa). zenon_intro zenon_H4fd. zenon_intro zenon_H4fc. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4fc). zenon_intro zenon_H4ff. zenon_intro zenon_H4fe. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H4fe). zenon_intro zenon_H6a. zenon_intro zenon_H500. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H500). zenon_intro zenon_H2d0. zenon_intro zenon_H501. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H501). zenon_intro zenon_H503. zenon_intro zenon_H502. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H502). zenon_intro zenon_H234. zenon_intro zenon_H504. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H504). zenon_intro zenon_H3dd. zenon_intro zenon_H505. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H505). zenon_intro zenon_H507. zenon_intro zenon_H506. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H506). zenon_intro zenon_H3e1. zenon_intro zenon_H508. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H508). zenon_intro zenon_H5e. zenon_intro zenon_H3d6. % 33.05/33.23 apply (zenon_and_s _ _ ax7). zenon_intro zenon_H50a. zenon_intro zenon_H509. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H509). zenon_intro zenon_H50c. zenon_intro zenon_H50b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H50b). zenon_intro zenon_H14e. zenon_intro zenon_H50d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H50d). zenon_intro zenon_H50f. zenon_intro zenon_H50e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H50e). zenon_intro zenon_Hf9. zenon_intro zenon_H153. % 33.05/33.23 apply (zenon_and_s _ _ ax8). zenon_intro zenon_H511. zenon_intro zenon_H510. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H510). zenon_intro zenon_H513. zenon_intro zenon_H512. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H512). zenon_intro zenon_H21c. zenon_intro zenon_H514. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H514). zenon_intro zenon_H516. zenon_intro zenon_H515. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H515). zenon_intro zenon_H83. zenon_intro zenon_H220. % 33.05/33.23 apply (zenon_and_s _ _ ax10). zenon_intro zenon_H1ca. zenon_intro zenon_H517. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H517). zenon_intro zenon_Hfd. zenon_intro zenon_H518. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H518). zenon_intro zenon_H1cb. zenon_intro zenon_H519. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H519). zenon_intro zenon_He4. zenon_intro zenon_H51a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H51a). zenon_intro zenon_H313. zenon_intro zenon_H51b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H51b). zenon_intro zenon_H19e. zenon_intro zenon_H51c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H51c). zenon_intro zenon_Hb1. zenon_intro zenon_H51d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H51d). zenon_intro zenon_He5. zenon_intro zenon_H51e. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H51e). zenon_intro zenon_H171. zenon_intro zenon_H51f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H51f). zenon_intro zenon_H175. zenon_intro zenon_H520. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H520). zenon_intro zenon_H1c3. zenon_intro zenon_H521. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H521). zenon_intro zenon_He9. zenon_intro zenon_H522. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H522). zenon_intro zenon_H312. zenon_intro zenon_H523. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H523). zenon_intro zenon_H525. zenon_intro zenon_H524. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H524). zenon_intro zenon_H3a5. zenon_intro zenon_H526. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H526). zenon_intro zenon_H172. zenon_intro zenon_H527. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H527). zenon_intro zenon_H3b9. zenon_intro zenon_H174. % 33.05/33.23 apply (zenon_and_s _ _ ax11). zenon_intro zenon_H2a4. zenon_intro zenon_H528. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H528). zenon_intro zenon_H87. zenon_intro zenon_H529. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H529). zenon_intro zenon_H2a5. zenon_intro zenon_H52a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H52a). zenon_intro zenon_H6f. zenon_intro zenon_H52b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H52b). zenon_intro zenon_H279. zenon_intro zenon_H52c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H52c). zenon_intro zenon_H52e. zenon_intro zenon_H52d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H52d). zenon_intro zenon_H38. zenon_intro zenon_H52f. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H52f). zenon_intro zenon_H70. zenon_intro zenon_H530. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H530). zenon_intro zenon_H248. zenon_intro zenon_H531. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H531). zenon_intro zenon_H243. zenon_intro zenon_H532. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H532). zenon_intro zenon_H247. zenon_intro zenon_H533. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H533). zenon_intro zenon_H74. zenon_intro zenon_H534. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H534). zenon_intro zenon_H31f. zenon_intro zenon_H535. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H535). zenon_intro zenon_H2d1. zenon_intro zenon_H536. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H536). zenon_intro zenon_H244. zenon_intro zenon_H537. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H537). zenon_intro zenon_H239. zenon_intro zenon_H538. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H538). zenon_intro zenon_H539. zenon_intro zenon_H246. % 33.05/33.23 apply (zenon_and_s _ _ ax12). zenon_intro zenon_H93. zenon_intro zenon_H53a. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H53a). zenon_intro zenon_H90. zenon_intro zenon_H126. % 33.05/33.23 apply (zenon_and_s _ _ ax13). zenon_intro zenon_H1a. zenon_intro zenon_H53b. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H53b). zenon_intro zenon_H17. zenon_intro zenon_H1dd. % 33.05/33.23 apply (zenon_and_s _ _ ax17). zenon_intro zenon_H334. zenon_intro zenon_H53c. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H53c). zenon_intro zenon_H108. zenon_intro zenon_H53d. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H53d). zenon_intro zenon_H2fb. zenon_intro zenon_H2fe. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_G). zenon_intro zenon_H53f. zenon_intro zenon_H53e. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H53e). zenon_intro zenon_H541. zenon_intro zenon_H540. % 33.05/33.23 apply (zenon_notor_s _ _ zenon_H540). zenon_intro zenon_H543. zenon_intro zenon_H542. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H542); [ zenon_intro zenon_H10b | zenon_intro zenon_H544 ]. % 33.05/33.23 apply (zenon_L140_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H544); [ zenon_intro zenon_H2fd | zenon_intro zenon_H545 ]. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.05/33.23 apply (zenon_L24_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.05/33.23 apply (zenon_L190_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.05/33.23 apply (zenon_L127_); trivial. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.23 apply (zenon_L200_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.23 apply (zenon_L9_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.23 apply (zenon_L201_); trivial. % 33.05/33.23 apply (zenon_L139_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H545); [ zenon_intro zenon_H328 | zenon_intro zenon_H546 ]. % 33.05/33.23 apply (zenon_L210_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H546); [ zenon_intro zenon_H335 | zenon_intro zenon_H547 ]. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H2a4); [ zenon_intro zenon_H86 | zenon_intro zenon_H2a6 ]. % 33.05/33.23 apply (zenon_L24_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H2a6); [ zenon_intro zenon_H2a8 | zenon_intro zenon_H2a7 ]. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2a8). zenon_intro zenon_H2aa. zenon_intro zenon_H2a9. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2a9). zenon_intro zenon_H2ac. zenon_intro zenon_H2ab. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2ab). zenon_intro zenon_H223. zenon_intro zenon_H2ad. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.23 apply (zenon_L215_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.23 apply (zenon_L9_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.23 apply (zenon_L217_); trivial. % 33.05/33.23 apply (zenon_L23_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H2a7); [ zenon_intro zenon_H27f | zenon_intro zenon_H2ae ]. % 33.05/33.23 apply (zenon_L127_); trivial. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2ae). zenon_intro zenon_H285. zenon_intro zenon_H2af. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2af). zenon_intro zenon_H2b1. zenon_intro zenon_H2b0. % 33.05/33.23 apply (zenon_and_s _ _ zenon_H2b0). zenon_intro zenon_H293. zenon_intro zenon_H2a3. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H87); [ zenon_intro zenon_H14 | zenon_intro zenon_H8c ]. % 33.05/33.23 apply (zenon_L218_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H8c); [ zenon_intro zenon_H35 | zenon_intro zenon_H8d ]. % 33.05/33.23 apply (zenon_L9_); trivial. % 33.05/33.23 apply (zenon_or_s _ _ zenon_H8d); [ zenon_intro zenon_H68 | zenon_intro zenon_H84 ]. % 33.05/33.23 apply (zenon_L219_); trivial. % 33.05/33.23 apply (zenon_L139_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H547); [ zenon_intro zenon_H341 | zenon_intro zenon_H548 ]. % 33.05/33.23 apply (zenon_L220_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H548); [ zenon_intro zenon_H34c | zenon_intro zenon_H549 ]. % 33.05/33.23 apply (zenon_L222_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H549); [ zenon_intro zenon_H353 | zenon_intro zenon_H54a ]. % 33.05/33.23 apply (zenon_L230_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H54a); [ zenon_intro zenon_H361 | zenon_intro zenon_H54b ]. % 33.05/33.23 apply (zenon_L238_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H54b); [ zenon_intro zenon_H373 | zenon_intro zenon_H54c ]. % 33.05/33.23 apply (zenon_L248_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H54c); [ zenon_intro zenon_H37c | zenon_intro zenon_H54d ]. % 33.05/33.23 apply (zenon_L256_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H54d); [ zenon_intro zenon_H38e | zenon_intro zenon_H54e ]. % 33.05/33.23 apply (zenon_L261_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H54e); [ zenon_intro zenon_H399 | zenon_intro zenon_H54f ]. % 33.05/33.23 apply (zenon_L269_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H54f); [ zenon_intro zenon_H3ac | zenon_intro zenon_H550 ]. % 33.05/33.23 apply (zenon_L272_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H550); [ zenon_intro zenon_H3c4 | zenon_intro zenon_H551 ]. % 33.05/33.23 apply (zenon_L274_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H551); [ zenon_intro zenon_H3d0 | zenon_intro zenon_H552 ]. % 33.05/33.23 apply (zenon_L281_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H552); [ zenon_intro zenon_H3e7 | zenon_intro zenon_H553 ]. % 33.05/33.23 apply (zenon_L282_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H553); [ zenon_intro zenon_H3ed | zenon_intro zenon_H554 ]. % 33.05/33.23 apply (zenon_L283_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H554); [ zenon_intro zenon_H3ef | zenon_intro zenon_H555 ]. % 33.05/33.23 apply (zenon_L284_); trivial. % 33.05/33.23 apply (zenon_notand_s _ _ zenon_H555); [ zenon_intro zenon_H3f3 | zenon_intro zenon_H3f9 ]. % 33.05/33.23 apply (zenon_L285_); trivial. % 33.05/33.23 apply (zenon_L286_); trivial. % 33.05/33.23 Qed. % 33.05/33.23 % SZS output end Proof % 33.05/33.23 (* END-PROOF *) % 33.05/33.23 nodes searched: 1447601 % 33.05/33.23 max branch formulas: 1865 % 33.05/33.23 proof nodes created: 15031 % 33.05/33.23 formulas created: 721491 % 33.05/33.23 %------------------------------------------------------------------------------